University of London

MSci Intercollegiate Planning Board

Physics MSci

Student Handbook

Intercollegiate taught courses for 2012-2013 session

This version is correct as at 9 October 2012.

Contents
Courses and Teachers .................................................................................................... 3
Web and Email Addresses ............................................................................................. 5
Programme Strands ........................................................................................................ 7
Teaching and Examination Arrangements ..................................................................... 8
College and Class Locations ........................................................................................ 11
King’s College, Strand. London, WC2. ................................................................... 11
Queen Mary University of London, Mile End Road, London E1. .......................... 12
Royal Holloway University of London, central London base. ................................ 13
Royal Holloway University of London, Egham campus ......................................... 14
University College, Gower Street, London WC1 .................................................... 15
Course Details .............................................................................................................. 16
4201 Mathematical Methods for Theoretical Physics ............................................ 16
4205 Lie Groups and Lie Algebras ......................................................................... 17
4211 Statistical Mechanics ..................................................................................... 18
4226 Advanced Quantum Theory ........................................................................... 19
4242 Relativistic Waves and Quantum Fields ........................................................ 21
4245 Advanced Quantum Field Theory.................................................................. 22
4261 Electromagnetic Theory .................................................................................. 23
4319 Formation and Evolution of Stellar Systems ................................................. 25
4421 Atom and Photon Physics .............................................................................. 27
4425 Advanced Photonics........................................................................................ 29
4427 Quantum Computation and Communication ................................................. 30
4431 Molecular Physics .......................................................................................... 31
4442 Particle Physics .............................................................................................. 32
4450 Particle Accelerator Physics .......................................................................... 34
4472 Order and Excitations in Condensed Matter .................................................. 35
4473 Theoretical Treatments of Nano-systems ...................................................... 37
4475 Physics at the Nanoscale ................................................................................ 39
4478 Superfluids, Condensates and Superconductors ............................................. 41
4501 Standard Model Physics and Beyond ............................................................. 43
4512 Nuclear Magnetic Resonance ........................................................................ 44
4515 Computing and Statistical Data Analysis ...................................................... 45
4534 String Theory and Branes .............................................................................. 46
4541 Supersymmetry and Gauge Symmetry .......................................................... 47
4600 Stellar Structure and Evolution ...................................................................... 48

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4601 Advanced Cosmology .................................................................................... 49
4602 Relativity and Gravitation .............................................................................. 50
4603 General Relativity and Cosmology ................................................................. 51
4605 Astroparticle Cosmology ................................................................................ 52
4630 Planetary Atmospheres .................................................................................. 53
4640 Solar Physics .................................................................................................. 54
4650 Solar System .................................................................................................. 55
4660 The Galaxy ..................................................................................................... 56
4670 Astrophysical Plasmas ................................................................................... 57
4680 Space Plasma and Magnetospheric Physics ................................................... 58
4690 Extrasolar Planets and Astrophysical Discs ................................................... 59
4702 Environmental Remote Sensing ..................................................................... 60
4800 Molecular Biophysics .................................................................................... 62
4810 Theory of Complex Networks ....................................................................... 65
4820 Equilibrium Analysis of Complex Systems ................................................... 66
4830 Dynamical Analysis of Complex Systems ..................................................... 67
4840 Mathematical Biology.................................................................................... 68
4850 Elements of Statistical Learning .................................................................... 69

2
 Courses and Teachers

Each course has a code number used by the Intercollegiate MSci board, shown at the
left hand side. Colleges use local codes for the courses they teach. The number is
usually the same as the MSci code, but some are different; beware! Local course
codes are shown at the right hand side.

All courses are a half course unit (15 credits). In QMUL language, they are a full
course unit.

The list shows the course title and the term in which it is taught. Also indicated is the
course teacher and the college from where he/she comes.

No. Course Title Term Teacher Local no

4201 Math Methods for Theoretical 1 Prof S. Sarkar KCL 7CCP4201
Physics
4205 Lie Groups and Lie Algebras € 1 Dr. A. Recknagel KCL+ 7CCMMS01
4211 Statistical Mechanics 2 Prof. B. Cowan RHUL§ PH4211
4226 Advanced Quantum Theory 1 Dr. D. Browne UCL PHASM426
4242 Relativistic Waves & Quantum 1 Dr. R.Russo QMUL PHY7004U
Fields
4245 Advanced Quantum Field Theory 2 Dr. A Brandhuber QMUL PHY7416
4261 Electromagnetic Theory 1 Prof. S. Thomas QMUL PHY7966
4319 Formation and Evolution of Stellar 1 Dr. I. Ferreras UCL PHASM319
Clusters
4421 Atom and Photon Physics 1 Dr. C. Faria UCL PHASM421
4425 Advanced Photonics 2 Prof. A. Zayats KCL 7CCP4126
4427 Quantum Computation and 2 Dr. A. Serafini UCL PHASM427
Communication
4431 Molecular Physics 2 Prof. A. Shluger UCL PHASM431
4442 Particle Physics 1 Dr. R. Nichol UCL PHASM442
4450 Particle Accelerator Physics 1 Dr. P. Karataev RHUL§ PH4450
4472 Order and Excitations in Condensed 2 Prof N Skipper UCL PHASM472
Matter
4473 Theoretical Treatments of Nano- 2 Dr. R. D’Agosta KCL 7CCP4473
systems
4475 Physics at the Nanoscale 1 Prof. V. Petrashov RHUL PH4475
4478 Superfluids, Condensates and 1 Prof. J. Saunders RHUL PH4478
Superconductors
4501 Standard Model Physics and 2 Prof. Mavromatos KCL 7CCP4501
Beyond
4512 Nuclear Magnetic Resonance 2 Dr. C. P. Lusher RHUL* PH4512
4515 Computing and Statistical Data 1 Prof. G. Cowan RHUL PH4515
Analysis
4534 String Theory and Branes € 2 Prof. P. West KCL+ 7CMMS34
4541 Supersymmetry & Gauge Symmetry 2 Dr S Schafer-Nameki KCL+ 7CMMS41
€
4600 Stellar Structure and Evolution 1 Dr. S. Vorontsov QMUL PHY7009U

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4601 Advanced Cosmology 1$Dr. J.E.Lidsey QMUL PHY7010U
4602 Relativity and Gravitation # 1Dr. A. G. Polnarev QMUL PHY706P
4604 General Relativity and Cosmology 2Prof. N. Mavromatos KCL 7CCP4630
4605 Astroparticle Cosmology 2Prof. M. KCL 7CCP4600
Sakellariadou
4630 Planetary Atmospheres 2 Prof. A. Coates UCL PHASM312

4640 Solar Physics 2 Dr. L van Driel & Dr. UCL PHASM314
I. Phillips (change
TBA)
4650 Solar System 1 Dr. C. Murray QMUL PHY7011U
4660 The Galaxy 2 Dr. W Sutherland QMUL PHY7012U
4670 Astrophysical Plasmas 2$ Prof. D. Burgess QMUL PHY7014U
4680 Space Plasma and Magnetospheric 2 Dr. A. Coates & UCL PHASM465
Physics Dr. C. Owen
4690 Extrasolar Planets & Astrophysics 2$ Prof. R. Nelson QMUL PHY7013U
Discs
4702 Environmental Remote Sensing 1 Prof M Wooster KCL† 7SSG5029
4800 Molecular Biophysics 2 Dr. B. Hoogenboom UCL PHASM800
4810 Theory of Complex Networks # 1 Dr. M. Urry KCL+ 7CCMCS02
4820 Equilibrium Analysis of Complex 1 Dr. I. Perez Castillo KCL+ 7CCMCS03
Systems
4830 Dynamical Analysis of Complex 2 Dr. A. Annibale KCL+ 7CCMCS04
Systems
4840 Mathematical Biology 2 Dr. R. Kuehn KCL+ 7CCMCS05
4850 Elements of Statistical Learning # 2 Dr. M. Urry KCL+ 7CCMCS06

Students will undertake one or more project-related courses in accordance

with practice at their own colleges.

Note: greyed-out courses will not run this session

§ Course taught over VideoCon network – sites at UCL, QMUL and RHUL
$ Course taught at QMUL in the evening this session.
* Course taught at RHUL in Egham, also available over VideoCon at QMUL
# Course unavailable to UCL students for syllabus reasons
+ Course taught by the Mathematics department of KCL
In the interest of balance students will ordinarily take no more than three KCL maths
courses.
†Course taught by the Geography department at KCL
€ Course content is mathematically demanding

4
 Web and Email Addresses

You can communicate with most of the course teachers using email. And some
courses have their own web pages. Address details are given in the following table.

No. Course and web address Teacher email address

4201 Math Methods for Theoretical Physics sarben.sarkar@kcl.ac.uk
4205 Lie Groups and Lie Algebras andreas.recknagel@kcl.ac.uk
http://www.mth.kcl.ac.uk/courses
4211 Statistical Mechanics b.cowan@rhul.ac.uk
http://personal.rhul.ac.uk/UHAP/027/PH4211/
4226 Advanced Quantum theory d.browne@ucl.ac.uk
4242 Relativistic Waves & Quantum Fields r.russo@qmul.ac.uk
http://ph.qmul.ac.uk/course/phy-415
4245 Advanced Quantum Field Theory a.brandhuber@qmul.ac.uk
4261 Electromagnetic Theory s.thomas@qmul.ac.uk
http://ph.qmul.ac.uk/course/phy-966
4319 Formation and Evolution of Stellar ipf@mssl.ucl.ac.uk
Clusters
4421 Atom and Photon Physics c.faria@.ucl.ac.uk
4425 Advanced Photonics a.zayats@kcl.ac.uk
4427 Quantum Computation and a.serafini@ucl.ac.uk
Communication
4431 Molecular Physics a.shluger@ucl.ac.uk
4442 Particle Physics rjn@hep.ucl.ac.uk
http://www.hep.ucl.ac.uk/~markl/teaching/4442
4450 Particle Accelerator Physics pavel.karataev@rhul.ac.uk
4472 Order & Excitations in Cond. Matt. n.skipper@ucl.ac.uk
4473 Theoretical Treatments of Nano- roberto.dagosta@kcl.ac.uk
systems
http://www.kcl.ac.uk/kis/schools/phys_eng/physics/courses/CourseList/CP4473.htm
4475 Physics at the Nanoscale v.petrashov@rhul.ac.uk
4478 Superfluids, Condensates and j.saunders@rhul.ac.uk
Superconductors
4501 Standard Model Physics and Beyond nikolaos.mavromatos@kcl.ac.uk
4512 Nuclear Magnetic Resonance c.lusher@rhul.ac.uk
4515 Computing & Statist. Data Analysis g.cowan@rhul.ac.uk
http://www.pp.rhul.ac.uk/~cowan/stat_course.html
4534 String Theory and Branes peter.west@kcl.ac.uk
http://www.mth.kcl.ac.uk/courses
4541 Supersymmetry and Gauge Symmetry sakura.schafer-nameki@kcl.ac.uk
http://www.mth.kcl.ac.uk/courses
4600 Stellar Structure and Evolution S.V.Vorontsov@qmul.ac.uk
4601 Advanced Cosmology J.E.Lidsey@qmul.ac.uk
www.maths.qmul.ac.uk/~jel/ASTM108/index.html
4602 Relativity and Gravitation A.G.Polnarev@qmul.ac.uk
http://ph.qmul.ac.uk/intranet/undergraduates/module?id=81
4604 General Relativity and Cosmology nikolaos.mavromatos@kcl.ac.uk
4605 Astrophysical Cosmology Mairi.sakellariadou@kcl.ac.uk

5
4630 Planetary Atmospheres ajc@mssl.ucl.ac.uk
http://www.mssl.ucl.ac.uk/teaching/UnderGrad/4312.html
4640 Solar Physics idp@mssl.ucl.ac.uk
http://www.mssl.ucl.ac.uk/~lvdg/ lvdg@mssl.ucl.ac.uk
4650 Solar System c.d.murray@qmul.ac.uk
www.maths.qmul.ac.uk/~agnor/MAS423
4660 The Galaxy w.j.sutherland@qmul.ac.uk
www.maths.qmul.ac.uk/~jbj/teaching/msc-galaxy
4670 Astrophysical Plasmas D.Burgess@qmul.ac.uk
www.space-plasma.qmul.ac.uk/astroplasmas
4680 Space Plasma and Magnetospheric ajc@mssl.ucl.ac.uk
Physics cjo@mssl.ucl.ac.uk
http://www.mssl.ucl.ac.uk/teaching/UnderGrad/4665.html
4690 Extrasolar Planets and Astrophysical Discs R.P.Nelson@qmul.ac.uk
4702 Environmental Remote Sensing martin.wooster@kcl.ac.uk
4800 Molecular Biophysics b.hoogenboom@ucl.ac.uk
4810 Theory of Complex Networks matthew.urry@kcl.ac.uk
http://www.mth.kcl.ac.uk/courses
4820 Equilibrium Analysis of Complex Systems isaac.perez castillo@kcl.ac.uk
http://www.mth.kcl.ac.uk/courses
4830 Dynamical Analysis of Complex Systems alessia.annibale@kcl.ac.uk
http://www.mth.kcl.ac.uk/courses
4840 Mathematical Biology reimer.kuehn@kcl.ac.uk
http://www.mth.kcl.ac.uk/courses
4850 Elements of Statistical Learning matthew.urry@kcl.ac.uk
http://www.mth.kcl.ac.uk/courses

6
 Programme Strands

The table below gives a coherent base of courses for your registered programme and
specialization interests. It is strongly recommended that you choose one of these
programme strands, and then select other courses to make up your full complement.

You should also note that some courses, particularly the more mathematical ones may
require a high degree of mathematical ability – certainly more than would be
contained in a standard single-honours Physics programme. Such courses would be
appropriate for some joint degrees.

Recommended Courses

Strand Term 1 Term 2

Particle PH4226: Advanced Quantum Theory

Physics PH4442: Particle Physics
PH4515: Computing and Statistical
Data Analysis
PH4242: Relativistic Waves and
Quantum Fields
Condensed PH4226: Advanced Quantum Theory PH4211: Statistical Mechanics
Matter PH4475: Physics at the Nanoscale PH4472: Order and Excitations in
Condensed Matter
PH4512: Nuclear Magnetic
Resonance
Theoretical PH4226: Advanced Quantum Theory PH4211: Statistical Mechanics
Physics PH4261: Electromagnetic Theory PH4242: Relativistic Waves and
Quantum Fields
PH4245: Advanced Quantum Field
Theory
General list PH4226: Advanced Quantum Theory PH4211: Statistical Mechanics
/ Applied
Physics

7
 Teaching and Examination Arrangements

Teaching Term Dates: Courses are taught in eleven-week terms. For the session
2012-2013 the teaching dates are:

First term Monday 1 October – Friday 14 December 2012

Second term Monday 7 January – Friday 22 March 2013

Note: these teaching dates may not be the same as your College terms!

Some courses – particularly Astro courses at QMUL and Maths courses at KCL might
run according to the home College’s term dates. You should check dates with the
course leader.

MSci Administrative contact points at each College

KCL: James French, james.french@kcl.ac.uk, telephone 020 7848 2823
QMUL: Susan Benedict, s.benedict@qmul.ac.uk, telephone 0207 882 6959
RHUL: Gill Green, gill.green@rhul.ac.uk, telephone 01784 443506
UCL: Dr. Ian Furniss, if@star.ucl.ac.uk telephone 020 7679 3481

Registration
If you are taking courses at another College, it is very important that you fill out a
course registration form from that College (i.e. you must fill out a UCL form for UCL
taught courses, a KCL form for KCL taught courses and so on). If you do not fill out
these types of form for all of your courses at other colleges you will not have a place
in the examination hall. It is not enough to inform your home College of your
selection. You must complete the registration forms and submit them through your
own College administrator by the date specified by each College:

KCL: Beginning of October 2012

QMUL: 25 January 2013
RHUL: 30 September 2012 (undergraduates), 31 October 2012 (postgraduates)
UCL: Beginning of October 2012

If you drop a course at another College you should inform both your own College and
the administrative contact point at the College that runs the course.

Class locations
The timetable gives details of room locations; this is published separately from the
Handbook and it is also available on the Intercollegiate MSci web pages
http://www.rhul.ac.uk/physics/informationforcurrentstudents/msci4thyear/msci4thyea
r.htm.

8
Most courses are taught in lecture rooms at UCL. The exceptions are:

Courses taught at KCL

4201 Mathematical Methods for Theoretical Physics
4205 Lie Groups and Lie Algebras
4425 Advanced Photonics
4501 Standard Model Physics and Beyond
4534 String Theory and Branes
4541 Supersymmetry & Gauge Symmetry
4605 Astroparticle Cosmology
4792 Environmental Remote Sensing
4810 Theory of Complex Networks
4820 Equilibrium Analysis of Complex Systems
4830 Dynamical Analysis of Complex Systems
4840 Mathematical Biology
4850 Elements of Statistical Learning
4603 General Relativity and Cosmology

Courses taught at QMUL

4600 Stellar Structure and Evolution
4601 Advanced Cosmology
4602 Relativity and Gravitation
4603 Astrophysical Fluid Dynamics
4650 Solar System
4660 The Galaxy
4670 Astrophysical Plasmas
Some of these QMUL courses will be taught in the evening; check pages 3-4 and the
timetable for details.

Courses taught over VideoCon network – sites at UCL, QMUL and RHUL
4211 Statistical Mechanics
4450 Particle Accelerator Physics

Courses taught at RHUL – Egham campus and available over VideoCon at QMUL
4512 Nuclear Magnetic Resonance

Coursework policy
Some courses have coursework associated with them and others do not. The details
are given in the Course Descriptions below.

Examination arrangements
UCL Students: You will sit UCL and RHUL examinations at UCL. You will sit KCL
examinations at KCL and QMUL examinations at QMUL.

KCL Students: You will sit KCL and RHUL examinations at KCL. You will sit UCL
examinations at UCL and QMUL examinations at QMUL.

QMUL Students: You will sit QMUL and RHUL examinations at QMUL. You will sit
UCL examinations at UCL and KCL examinations at KCL.

9
RHUL students: You will sit all your examinations at RHUL.

The college responsible for the examination is given in column 5 of the table on pages
3 and 4.

Computer and Library facilities at UCL

Registration on any UCL course will get you automatic library access, a UCL
computer account and a UCL security card. This takes about a week from UCL
receiving your signed form and submitting it to their Exam section. The Exam section
then set all this up and will notify you when it is done.

10
 College and Class Locations

King’s College, Strand. London, WC2.

11
Queen Mary University of London, Mile End Road, London E1.

Stepney Green tube station is on the District and Hammersmith & City lines. Turn left
out of the station and walk along the Mile End road for approximately 5 minutes until
you reach the East Gate on your left.

Mile End tube station is on the Central line. Turn left out of the station, cross over the
junction, go under the bridge and along Mile End road for approximately 2 minutes.
You will see the East Gate on the opposite side of the road.

The East Gate will be recognisable by a big 'Queen Mary' banner on the wall next to
it.

Students may obtain a campus map from the Physics Department Secretarial office
on the second floor of the Physics Building in Rooms 210 or 211.

12
Royal Holloway University of London, central London base.
11 Bedford Square and 2 Gower Street. These are two adjacent buildings on the
corner of Bedford Square and Gower Street.

Euston
Warren (British Rail)
Street
Station Euston Eusto
Square n
Road
Station
Gower Pla
ce Endsleigh Gardens

Gordon Street

Taviton St.
Grafton Way

Gower
UCL
Cleveland

Maple Street University Street

Endsleigh Place
Tottenham

Tavistock Sq.
Gordon Sq.

Gordon Sq.
Street

Howland St.

Torringdon Place

Woburn Place
Bedford Way
Malet Street

Goodge
Street

Street Chenies St.

Station
Court

Russell
Store St. Square
Senate Station
Percy St. House
Bedford Square Montagu Place
Rathbone Place

Russell Sq.
Bloomsbury St.

Montague St.

Bedford Place

British
Road

Southamp

Museum
ton Row

Gt. Russell St.

Tottenham Court
Road Station

Royal Holloway
11 Bedford Sq. / 2 Gower St.
London WC1B 3RA

On arrival students must sign in at the front desk of the Bedford Square building
before proceeding to their class. The Gower Street building is kept locked; the course
teacher will obtain the key to the front door and students may need to ring the bell to
gain entrance.

13
Royal Holloway University of London, Egham campus

By Rail: There are frequent services from London Waterloo to Egham station (35
minutes); Woking to Egham (35 minutes, change at Weybridge) and Reading to
Egham (40 minutes). Services at weekends, especially those on Sunday, are less
frequent than on weekdays.

From Egham station by Bus: There is a College bus service that carries students and
visitors directly from Egham station to the bus stop on Campus. The bus timetable is
available on http://www.rhul.ac.uk/forstudents/campuslife/collegebusservice.aspx.

From Egham station by Foot: The College is just over a mile from Egham Station,
about 20 minutes walk. Turn right out of the station along Station road and walk
about 100 yards to the T-Junction and the traffic lights. Turn left at the junction and
follow the road up to the large roundabout; go left up Egham Hill (south-west
direction). It is easiest to enter by the gate before the foot bridge over the road and
follow the path to the Physics Department – buildings 21 and 22.

By Road: The College is on the A30, 20 miles from central London and about a mile
south-west of the town of Egham. It is 2 miles from junction 13 of the M25 (London
Orbital). After leaving the motorway take the A30 west, signposted to Bagshot and
Camberley (not Egham). At the first roundabout, take the second exit; at the second
roundabout, again take the second exit and continue on the A30 up Egham Hill. The
College is on the left at the top of the hill. There are footbridges across the road at the
pedestrian and main entrances.

14
University College, Gower Street, London WC1

Entrance to the UCL campus is from Gower Street into the Main Quadrangle and then
into the appropriate building.

15
 Course Details

4201 Mathematical Methods for Theoretical Physics

Aims and Objectives

This course introduces mathematical techniques which are crucial to the formulation
and solution of fundamental theories in Physics. It is biased towards the application of
mathematics to solve problems, rather than the development of rigorous mathematics.
It assumes competence in the use of mathematics covered in previous mathematical
courses given in the first and second years. On finishing the course, students should
be able to solve physics problems through complex analysis, the calculus of
variations, and extend the definition of special functions to the complex plane.

Syllabus outline
Functions of a complex variable: limits, continuous and differentiable functions;
Cauchy-Riemann equations for an analytic function f(z); physical significance of
analytic functions; properties of power series, definition of elementary functions using
power series; complex integral calculus, contour integrals, upper bound theorem for
contour integrals; Cauchy-Goursat theorem; Cauchy integral representation, Taylor
and Laurent series, singularities and residues; residue theorem and its applications.
Properties of the gamma function Γ(z). Bessel functions; series solution of the Bessel
differential equation; definition of Jn(z) and Yn(z); recurrence relations for Jn(z); zeros
of Jn(z); orthogonality properties of Bessel functions; solution of the wave equation in
plane polar coordinates. Classical mechanics; constraints and generalised co-
ordinates; D’Alembert’s principle; Lagrange equations of motion; conservation laws;
Hamilton's equation of motion; conservation laws and Poisson brackets. Calculus of
variation; method of Lagrange multipliers; functionals; Euler-Lagrange equation;
minimum surface energy of revolution; properties of soap films; Hamilton’s principle
in classical dynamics; multiple integral problems and field equations.

16
 4205 Lie Groups and Lie Algebras

Aims and objectives:

This course gives an introduction to the theory of Lie groups, Lie algebras and their
representations. Lie groups are essentially groups consisting of matrices satisfying
certain conditions (e.g. that the matrices should be invertible, or unitary, or
orthogonal). They arise in many parts of mathematics and physics. One of the
beauties of the subject is the way that methods from many different areas of
mathematics (algebra, geometry, analysis) are all brought in at the same time. The
course should enable you to go on to further topics in group theory, differential
geometry, string theory and other areas.

Syllabus:
Examples of Lie groups and Lie algebras in physics. Matrix Lie groups, matrix Lie
algebras, the exponential map, BCH formula. Abstract Lie algebras, examples: sl(2),
sl(3), Poincare algebra. Representations of Lie algebras, sub-representations, Schur's
Lemma, tensor products. Cartan-Weyl basis, classification of simple Lie algebras
(without proof).

Web page: See http://www.mth.kcl.ac.uk/courses-10-11/

Teaching arrangements:
Two hours of lectures per week

Prerequisites:
Note – A high level of mathematical ability is required for this course
Basic knowledge of vector spaces, matrices, groups, real analysis.

Assessment:
One two-hour written examination at the end of the academic year.
Assignments:
Exercises in the course notes. Solutions will be provided.

Books:
There is no book that covers all the material in the same way as the course, but the
following may be useful:
 Baker, Matrix groups, Springer, 2002
 J. Fuchs, C. Schweigert, Symmetries, Lie algebras and representations, CUP
1997
 J. Humphreys, Introduction to Lie Algebras and Representation Theory,
Springer, 1972
 H. Jones, Groups, Representations and Physics, IoP, 1998

17
 4211 Statistical Mechanics
Course taught over VideoCon network – sites at UCL, QMUL and RHUL

The Methodology of Statistical Mechanics (5 lectures)

 Relationship between statistical mechanics and thermodynamics – emergence.
 Review of equilibrium statistical mechanics.
 The grand canonical ensemble. Chemical potential. The Bose and Fermi
distribution functions.
 The classical limit, phase space, classical partition functions.

Weakly Interacting Systems (7 lectures)

 Non-ideal systems. The imperfect gas and the virial expansion, Mayer’s
f function and cluster integrals. (2 lectures)
 The second virial coefficient for the hard sphere, square-well and Lennard-Jones
potentials. (2 lectures)
 Throttling and the Joule-Kelvin coefficient. (1 lecture)
 The van der Waals gas as a mean field paradigm. (2 lectures)

Strongly Interacting Systems (13 lectures)

 The phenomenology of phase transitions, definitions of critical exponents and
critical amplitudes. (2 lectures)
 Scaling theory, corresponding states. (2 lectures)
 Introduction to the Ising model. Magnetic case, lattice gas and phase separation in
alloys and Bragg-Williams approximation. Transfer matrix method in 1D. (3
lectures)
 Landau theory. Symmetry breaking. Distinction between second order and first
order transitions. Discussion of ferroelectrics. (3 lectures)
 Broken symmetry, Goldstone bosons, fluctuations, scattering, Ornstein Zernike,
soft modes. (3 lectures)

Dissipative Systems (5 lectures)

 Fluctuation-dissipation theorem, Brownian motion, Langevin equation, correlation
functions. (5 lectures)

Books:
B. Cowan, “Topics in Statistical Mechanics”, 2005, Imperial College Press.
R. Bowley & M. Sánchez, “Introductory Statistical Mechanics”, 1999, OUP
Other books and publications will be referred to by the lecturer.
Course notes and other material available on the course web pages at
http://personal.rhul.ac.uk/UHAP/027/PH4211/

Assessment:
Written examination of 2½ hours contributing 90%, coursework contributing 10%.

18
 4226 Advanced Quantum Theory

This course aims to:

 review the basics of quantum mechanics so as to establish a common body of
knowledge for the students from the different Colleges on the Intercollegiate
MSci. programme;
 extend this, by discussing these basics in more formal mathematical terms;
 explore the WKB approximation, as a method for studying tunnelling and
quantum wells;
 explore advanced topics in the dynamics of quantum systems; including time-
dependent perturbation theory, and the dynamics of open quantum systems;
 provide students with the techniques and terminology which they can apply in
specialist courses and in their research projects.

Syllabus: (Approximate allocation of lectures is shown in brackets below)

Formal quantum mechanics [10.5 hours]

[Partly revision] Abstract vector spaces; norm, inner product, basis, linear functionals,
operators, column vector and matrix representations of abstract vectors and operators,
Dirac notation, Hermitian and unitary operators, projectors. Expectation values.
Postulates of quantum mechanics.
Representations of continuous variables, position and momentum.
Compound systems, tensor product, entanglement.
Statistical state preparation and mixed states, density operator formalism, density
operators to describe sub-systems of entangled systems

Advanced wave mechanics - WKB approximation [4.5 hours]

WKB Ansatz and derivation of WKB approximation wave-functions. The failure of
these wave-functions at classical turning points. The role of connection formulae.
Application to quantum wells and quantum tunnelling in one-dimension.

Atoms, light and their interaction [3 hours]

[Revision of] Quantum Harmonic oscillator, Wave equation and quantisation of light.
Optical cavities and concept of a light mode. Two-level atom and dipole
approximation. Rotating Wave Approximation and Jaynes-Cummings model.

Advanced topics in time-dependence 1 - Unitary Evolution [3 hours]

Unitary evolution under the Schrödinger equation, Split operator method and
Tsuzuki-Trotter decomposition. Heisenberg picture, Interaction picture. Example:
Jaynes-Cummings model in the interaction picture.

Advanced topics in time-dependence 2) - Time-dependent perturbation theory [6 hours]

Dirac’s method as application of interaction picture. Time-dependent perturbation
theory. First-order time-dependent perturbation theory. Higher-order time-dependent
theory. Examples: constant perturbation and harmonic perturbation. Fermi's Golden
Rule with examples of its application.

19
Advanced topics in time-dependence 3) - Open quantum systems [6 hours]
Von Neumann equation for density matrices. Interaction with enviroment. Evolution
of a sub-system. Markov approximation.
Abstract approach to non unitary evolution. Completely positive maps. Kraus
operators.
Master equations. Lindblad form, derivation from Kraus operator Ansatz. Quantum
trajectories and jump operators. Example: Damped quantum harmonic oscillator.

Books:
Those which are closest to the material and level of the course are (in alphabetical
order)
 B.H. Bransden and C.J.Joachain, Introduction to Quantum Mechanics, Longman
(2nd Ed, 2000), ) (available at a discount from the physics departmental Tutor),
 C.Cohen-Tannoudji, B.Diu and F.Laloe, Quantum Mechanics, (2 Vols) Wiley,
 S.Gasiorowicz, Quantum Physics, Wiley, (1996)
 F.Mandl, Quantum Mechanics, Wiley (1992)
 E.Merzbacher, Quantum Mechanics, (3rd Ed.) Wiley, (1998)
 M. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory
Addison Wesley
 J. J. Sakurai, Modern Quantum Mechanics, Addison Wesley, (2010)

John Preskill (Caltech) Lecture notes on Quantum Computation,

Chapter 2, "States and Ensembles"
http://www.theory.caltech.edu/people/preskill/ph229/notes/chap2.pdf
Chapter 3, "Measurement and evolution"
http://www.theory.caltech.edu/people/preskill/ph229/notes/chap3.pdf

Assessment: Examination of 2½ hours duration contributing 90%, coursework 10%.

Prerequisites:
Students will be expected to have attended and passed their department's introductory
and intermediate quantum mechanics course. For example, at UCL these will be
PHAS2222: Quantum Physics and PHAS3226: Quantum Mechanics.

The following topics will be assumed to have been covered:

 Introductory material: states, operators and time-independent Schrödinger
equation, the Born interpretation of the wave function, transmission and
reflection coefficients, Dirac notation
 Harmonic oscillator: energy eigenvalues, ladder operators
 Time-independent perturbation theory: including the non-degenerate and
degenerate cases and its application to the helium atom ground state, Zeeman
effect and spin-orbit interactions.

This is a theory course with a strong mathematical component to this course, and
students should feel confident in their ability to learn and apply new mathematical
techniques.

20
 4242 Relativistic Waves and Quantum Fields

Classical field theories, Special Relativity and Quantum Mechanics (part revision):

Elements of Classical field theories: variational principle, equations of motion and

Noether theorem.

Short introduction to Special Relativity: 4-vector notation, Lorentz transformations,

Lorentz invariance/covariance.

Quantum Mechanics: Schroedinger equation, wavefunctions, operators/observables,

symmetries and conservation laws in QM, Fock space for non-relativistic theories

Relativistic Wave equations:

Klein-Gordon equation: plane wave solutions, positive and

negative energy solutions.

Dirac equation: Gamma matrices in 4D (Dirac, Weyl and Majorana

representations); Gamma matrices in 2D and 3D; Lorentz transformations and
covariance of Dirac equation: non-relativistic limit, Dirac equation in an
electromagnetic field; discrete symmetries: C & P & T symmetry

Quantum Field Theory:

Scalar fields: canonical quantisation and Fock space interpretation of the

free complex and real Klein-Gordon field; vacuum energy; Causality,
commutators and time ordered products, the Feynman propagator; Dyson
expansion; S-matrix, tree-level scattering amplitudes; examples of an
interacting scalar theory with three flavours; Wick's theorem.
Quantisation of Dirac fermions: spin-statistics connection.

Prerequisites: a 3rd year quantum mechanics course; familiarity with the

Lagrangian formalism and with the four vector notation in Special
Relativity

Books:

F. Mandl and G. Shaw, Quantum Field Theory, John Wiley and Sons Ltd
M. Peskin, D. Schroeder, An Introduction to Quantum Field Theory, Addison
Wesley
L.H. Ryder, Quantum Field Theory, Cambridge University Press

Assessment:
Written examination of 2½ hours contributing 90%, coursework contributing 10%.

21
 4245 Advanced Quantum Field Theory

Building on the fundamental concepts of Quantum Field Theory introduced in 4242

Relativistic Waves and Quantum Fields, this course will cover the following topics:

1 Classical Field Theory and Noethers Theorem, Quantisation of free

spin 0, 1/2 and 1 fields (revision)

2 Perturbation Theory and Feynman Diagrams:

Dyson formula and the S-matrix, in and out states, evaluation of S-matrix elements
using Wick’s theorem and LSZ reduction formula, formulation in terms of Feynman
diagrams (part revision)

3 Quantum Electrodynamics
Feynman diagrams for QED, simple scattering processes at tree level such as e– e– and
e– e+ scattering, cross sections, spin sums

4 Renormalisation:
Renormalisation of φ4 and QED at one-loop level, regularisation (dimensional and
Pauli-Villars), Running coupling, corrections to electron anomalous moment

5 If time permits:
Elements of non-Abelian gauge theories, path integrals and ghosts, anomalies,
modern, twistor inspired methods to calculate amplitudes.

Four sessions will be devoted to a discussion of coursework problems and their

solutions.

Prerequisites: 4242 Relativistic Waves and Quantum Fields

Books:
F. Mandl and G. Shaw, Quantum Field Theory, John Wiley and Sons Ltd
L.H. Ryder, Quantum Field Theory, Cambridge University Press
J. Bjorken and S. Drell, Relativistic quantum mechanics and
Relativistic quantum fields, McGraw-Hill
S. Weinberg, The Quantum Theory of Fields, Volume I, Cambridge
University Press

Assessment:
Written examination of 2½ hours contributing 90%, coursework contributing 10%.

22
 4261 Electromagnetic Theory

 Revision of laws of electromagnetism in vacuo, displacement current, Maxwell’s

equations in vacuo, charge and current density sources, energy theorems, fluxes of
energy and momentum. (2 hours)

 Polarization and magnetization, D and H fields, linear media, boundary conditions

on the fields in media, Maxwell stress tensor, concept of macroscopic fields as
space averages of molecular fields, Lorentz local field argument, the Clausius-
Mossotti relation. (3 hours)

 Maxwell’s equations in media, Homogeneous wave equation in vacuo and in

media, concept of frequency dependent dielectric function (), properties of real
and imaginary parts of (), causality, Kramers-Krönig relation. (3 hours)

 Scalar and vector potentials, gauge transformations, inhomogeneous wave

equation, the retarded solution to the wave equation, radiation from a Hertzian
dipole with discussion of near and far fields, formula for power radiated,
qualitative discussion of magnetic dipole and electric quadrupole radiation.
(4 hours)

 Scattering of a plane wave by a single slowly moving charged particle, total and
differential scattering cross-sections, optical theorem, scattering from a medium
with space-varying dielectric constant, scattering from an assemblage of
polarizable particles, Rayleigh-Smoluchowski-Einstein theory of why the sky is
blue – critical opalescence. (5 hours)

 Lorentz transformations, charge and current density as a 4-vector, the potential

4-vector, tensors and invariants, the relativistic field tensor F, Lorentz
transformation properties of current density and potential 4-vectors and of the free
vacuum E and B fields, tensor form of Maxwell’s equations, covariant
formulation of energy and momentum theorems, energy-momentum tensor.
(5 hours)

 Liénard-Wiechert potentials for a moving charged particle derived from a delta-

function source, fields for a uniformly moving charged particle in the non-
relativistic and ultra-relativistic limits, radiation from accelerated charges, the
cases of velocity and acceleration parallel and perpendicular, Larmor formula for
radiated power, bremsstrahlung and synchrotron radiation as examples. (5 hours)

 Maxwell theory as a Lagrangian field theory, the free field as an ensemble of

oscillators. (3 hours)

23
Prerequisites:
The course assumes a knowledge of the electromagnetism topics as detailed in the
Institute of Physics Recommended Core. These comprise:

 Electrostatics: the electric field E

 Charge. Coulomb’s law, Gauss’s flux theorem
 Electrostatic potential; Poisson’s and Laplace’s equations
 The field and potential of a point charge and an electric dipole
 Capacitance and stored energy
 Magnetostatics: the magnetic field B
 Electric currents; the Biot-Savart law, Ampère’s circuital theorem
 The field of a linear current and of a magnetic dipole/current loop
 Lorentz force law, force on current-carrying conductors
 Motion of particles in electric and magnetic fields
 Electrodynamics: Faraday’s law, Lenz’s law and induction
 Inductance and stored magnetic energy
 Maxwell’s equations and electromagnetic waves
 The electromagnetic spectrum
 The Poynting vector
 Fields in media: D and H; permittivity, permeability and dielectric constant: basic
ideas, related to their microscopic origins
 Energy storage in media

In addition the following knowledge in mathematics and physics are assumed:

 Taylor series.
 Div, Grad and Curl, Surface and Volume integrals, Gauss and Stokes theorems.
 The complex representation of harmonically varying quantities.
 Fourier transforms.
 The one-dimensional wave equation.
 Matrix multiplication and familiarity with indices.
 Contour integration up to Cauchy’s theorem (this is used only in the discussion of
the Kramers-Krönig relation)
 From special relativity the explicit form of the simple Lorentz transformation
between frames in relative motion along a single coordinate direction.
 It is desirable but not necessary that students have met the Lagrangian formulation
of particle mechanics.
 We do not assume that students have met the concept of Green’s functions before.

Books:
J D Jackson, Classical Electrodynamics, J Wiley
H C Ohanian, Classical Electrodynamics, Allyn and Bacon

Assessment:
Written examination of 2½ hours contributing 90%, coursework contributing 10%.

24
 4319 Formation and Evolution of Stellar Systems

Aims of the Course

This course aims to:

 give a detailed description of the structure, physical characteristics, dynamics and

mechanisms that determine the kinematic structure, origin and evolution of
clusters and galaxies;
 discuss applications, including stellar clusters within the Galaxy, spiral and
elliptical galaxies and clusters of galaxies, with emphasis given to the
interpretation of observational data relating to the Milky Way.

Objectives
After completing this course students should be able to:

 identify the dynamical processes that operate within star clusters, galaxies and
clusters of galaxies;
 explain the observed characteristics of stellar motions within the Milky Way;
 use this information to elucidate the internal structure of the Galaxy;
 be able to discuss the dynamical structure and observational appearance of
clusters and external galaxies;
 understand how these objects have formed and are evolving.

Methodology and Assessment

30 lectures and 3 problem class/discussion periods.

Assessment is based on the results obtained in the final written examination (90%)
and three problem sheets (10%).

Textbooks
 Stellar Dynamics (I.R. King, W.H. Freeman, 1996)
 Galaxies: Structure and Evolution (R.J. Tayler, Cambridge Univ. Press, 1993)

Syllabus
(The approximate allocation of lectures to topics is shown in brackets below).

The observational properties of galaxies and clusters [1 lecture]

Historical introduction
Galaxy and cluster classification
Observational overview
The theoretical problem.

The mathematical foundations of stellar dynamics [3 lectures]

Stellar dynamics.
The equations of motion.
The Collisionless Boltzmann Equation (CBE)
The solution of the CBE.

25
 Time-independent solution of the CBE
Jeans’ theorem.
Using the distribution function

The Milky Way I: Individual motions [3 lectures]

Galactic coordinates and the Local Standard of Rest
Galactic rotation in the solar neighbourhood
The determination of Oort's constants
Differential motion and epicyclic orbits
Motion perpendicular to the galactic plane

The Milky Way II: The Collisionless Boltzmann Equation [3 lectures]

The CBE in galactic coordinates
The third integral
Probing deeper into the Galaxy
The Oort substitution
The Jeans' equations
The density distribution from individual orbits

Evolution of dynamical systems [4 lectures]

Relaxing assumptions
Two-body encounters and collisions
The relaxation timescale
The relative importance of close and distant encounters
Comparison with crossing time and age
The Fokker-Planck equation
Dynamical friction
The Kolmogorov-Feller equation
The virial theorem
Applications of the virial theorem

Stellar clusters [4 lectures]

Introduction
Entropy
Evaporation of clusters
Models of globular clusters
Tidal forces in globular clusters
Dynamical evolution of clusters
Other long-term evolutionary effects
The importance of binaries

Prerequisites
PHAS3136 - Cosmology and Extragalactic Astronomy

26
 4421 Atom and Photon Physics

Interaction of Light with atoms (single photon) (4 lectures)

1 Processes – excitation, ionization, auto-ionization
2 A and B coefficients (semi classical treatment)
3 Oscillator strengths and f-sum rule
4 Life times – experimental methods. (TOF and pulsed electron)
5 Review of selection rules
6. Photo-ionization – synchrotron radiation

L.A.S.E.R (3 lectures)
1 Line shapes g(); Pressure, Doppler, Natural
2 Absorption and Amplification of radiation
3 Population inversion; spontaneous and stimulated emission
4 YAG and Argon ion lasers
5 Tunable radiation – dye and solid
6 Mode structure

Chaotic Light and Coherence (2 lectures)

1 Line broadening
2. Intensity fluctuations of chaotic light
3 First order correlation functions
4. Hanbury Brown Twiss experiment

Laser Spectroscopy (3 lectures)

1 Optical pumping – orientation and alignment
2 Saturation absorption spectroscopy
3 Lamb shift of H(1S) and H(2S)
4 Doppler-Free spectroscopy

Multi-Photon Processes (3 lectures)

1 Excitation, ionization, ATI
2 Laser field effects – pondermotive potential – Stark shifts – Harmonic Generation
3 Pump and Probe Spectroscopy
4 Multi-photon interactions via virtual and real states
5 Two photon decay of hydrogen (2S–1S)
6 Simultaneous electron photon interactions

Light Scattering by Atoms (3 lectures)

1 Classical Theory
2 Thompson and Compton scattering
3 Kramers-Heisenberg Forumlae
4 (Rayleigh and Raman scattering)

27
Electron Scattering by Atoms (4 Lectures)
1 Elastic, inelastic and super-elastic
2 Potential scattering
3 Scattering amplitude – partial waves
4 Ramsauer-Townsend Effect – Cross Sections
5 Resonance Structure

Coherence and Cavity Effects in Atoms (4 lectures)

1 Quantum beats – beam foil spectroscopy
2 Wave packet evolution in Rydberg states
3 Atomic decay in cavity
4. Single atom Maser

Trapping and Cooling (4 lectures)

1 Laser cooling of atoms
2 Trapping of atoms
3 Bose condensation
4 Physics of cold atoms – Atomic Interferometry

Books:
A Thorne, “Spectrophysics”, (Chapman and Hall)
J Wilson and J F B Hawkes, “Opto Electronics”, (Prentice Hall)

Assessment: Examination of 2½ hours duration contributing 90%, coursework 10%.

28
 4425 Advanced Photonics
Module pre-requisites
Electromagnetism and optics at a typical second year level is essential. Quantum
mechanics and condensed matter physics at a typical third year level is desirable but
not essential.

Syllabus outline
Summary of those aspects of quantum theory, optics and materials science as applied
in photonics. A survey of the main types of photonic applications and concepts.
Optical fibres and communication systems. Basic understanding of physics of
subwavelength light manipulation (silicon photonics, photonic crystals, plasmonics,
metamaterials). Modern applications of photonics (information processing, optical
data storage, biophotonics and sensing, energy).

Aims and Objectives

The aim of the course is to provide a comprehensive overview of theoretical and
practical aspects of major modern photonic technologies with special emphasis on
novel trends and applications of nanophotonics.
The students should be exposed to modern concepts in photonics, understand main
physics principles behind modern photonic technologies, such as optical
communications, nanophotonics, plasmonics, metamaterials, biosensing and bio-
imaging and their applications in everyday life.

The successful student should be able to:

Demonstrate comprehension of the concepts of photonics. Apply these concepts to a
range of physical situations, solving simplified model problems
Show the linking of the basic and advanced concepts within the above subject area
problem formulation and solving (both numerical and symbolic), written and verbal
communication skills, group work

29
 4427 Quantum Computation and Communication

Background [3]: The qubit and its physical realization; Single qubit operations and
measurements; The Deutsch algorithm; Quantum no-cloning.

Quantum Cryptography [3]: The BB84 quantum key distribution

protocol; elementary discussion of security; physical implementations of kilometers.

Quantum Entanglement [8]: State space of two qubits; Entangled states; Bell’s
inequality; Entanglement based cryptography; Quantum Dense Coding; Quantum
Teleportation; Entanglement Swapping; Polarization entangled photons &
implementations; von-Neumann entropy; Quantification of pure state entanglement.

Quantum Computation [8]: Tensor product structure of the state space of many
qubits; Discussion of the power of quantum computers; The Deutsch-Jozsa algorithm;
Quantum simulations; Quantum logic gates and circuits; Universal quantum gates;
Quantum Fourier Transform; Phase Estimation; Shor’s algorithm; Grover’s algorithm.

Decoherence & Quantum Error Correction [4]: Decoherence; Errors in quantum

computation & communication; Quantum error correcting codes; Elementary
discussion of entanglement concentration & distillation.

Physical Realization of Quantum Computers [4]: Ion trap quantum computers;

Solid state implementations (Kane proposal as an example); NMR quantum computer.

Books:

Assessment: Examination of 2½ hours duration contributing 90%, coursework 10%.

Prerequisites: Third year level quantum mechanics.

30
 4431 Molecular Physics

1. Atomic Physics (2 lectures)

Brief recap of atomic physics: n, l, m, s; He atom, orbital approximation, exchange.

2. Molecular electronic structure (8 lectures):

The molecular Hamiltonian and the Born-Oppenheimer approximation.
Electronic structure, ionic and covalent bonding, Bonding in H2+ and H2. Muon
catalysed fusion. Dissociation and united atom limits. Long range forces.

3. Nuclear motion (6 lectures)

Vibrational structure: harmonic motion and beyond, energy levels and wavefunctions
Rotational structure: rigid rotor and energy levels Energy scales within a molecule:
ionisation and dissociation. Nuclear spin effects. Labeling schemes for electronic,
vibrational and rotational states.

4. Molecular spectra (7 lectures):

Microwave, infrared and optical spectra of molecules. Selection rules, Franck-Condon
principle. Experimental set-ups. Examples: the CO2 laser, stimulated emission
pumping experiment. Raman spectroscopy. Ortho-para states. Absorption spectra of
simple diatomics (eg O2 and NO, N2). Simple poly-atomics (ozone, water).

5. Molecular processes (7 lectures):

Collisions with electrons. Elastic and inelastic collisions. Dissociation, dissociative
attachment and dissociative recombination. Resonances and negative ions.
Experimental techniques. Theoretical models (briefly).

Prerequisites: Quantum Physics (year 2/3), Atomic Physics (year 2/3), some previous
experience of basic molecular physics would be helpful but is not a requirement.

Books:
P W Atkins and R S Friedman, Molecular Quantum Mechanics, (Oxford University)
B H Bransden and C J Joachain, Physics of Atoms and Molecules, (Longman, 1983)
C.W. Banwell and E. McGrath, Fundamentals of Molecular Spectroscopy, 4th Edition,
(McGraw-Hill, 1994)

Assessment:
Examination of 2½ hours duration contributing 90%, coursework 10%.

31
 4442 Particle Physics
Basic Concepts
Four vector notation, invariants and natural units. Feynman diagrams as a tool for
qualitative description of interactions. Cross sections, differential cross sections and
luminosity. The Mandelstam variables s, t and u for scattering. The family of
fundamental particles: leptons and quarks and vector bosons. Interactions of leptons
and quarks, summarised in terms of characteristic decay times, ranges and the
mediating bosons. Yukawa field.

Relativistic QM
Relativistic wave equations (Klein-Gordon, Dirac). Negative energy solutions and the
Feynmann-Stuckelberg interpretation. Conserved Current and Propagators. Invariant
amplitude.

Symmetries and conservation laws.

Translational invariance and momentum conservation as a worked example.
Symmetries of the Strong and Electromagnetic Interactions: Relation between
symmetry, invariance and conservation laws; parity (invariance of Hamiltonian,
fermions and antifermions, quarks and hadrons). Higgs mechanism and spontaneous
symmetry breaking.

Particle Detectors
These will be covered as an integral part of the study of current experiments. Basic
principles of calorimeters, drift chambers and silicon vertex detectors.

Leptons and Hadrons

Discovery of leptons. Evidence for lepton universality, lepton number conservation.
Parity, C Symmetry. Quarks, and hadrons. Multiplets and Quark diagrams.
Resonances. Breit-Wigner formula.

Quarks and QCD

Colour. Confinement. Screening, Asymptotic freedom and Jets. Rhad for e+e
annihilation. 2- and 3-jet events. The discovery of the top quark through the
measurement of jets at the CDF detector at Fermilab, including a look at basic
calorimetry.

More on Leptons, and Weak Interactions

Discovery and properties of W and Z bosons. Quark and lepton doublets and Cabibbo
mixing. Comparing the weak and electromagnetic couplings. Parity and C-Parity
violation and handedness of neutrinos. The measurement of Z width at LEP.
Electroweak Theory: Unification of weak and electromagnetic. Gauge
transformations.

Deep Inelastic Scattering

Elastic electron-proton scattering. Deep Inelastic scattering. Scaling and the quark
parton model. Factorisation. Scaling violations and QCD. Triggering at HERA.
Measurement of proton structure at HERA. Neutral and Charged Currents at HERA.

32
The Standard Model and What Next?
Some idea of current open questions. Neutrino oscillations, running couplings, SUSY.
Cosmological connections – dark matter, CP violation, very high energy cosmic rays.

Prerequisites: 4241 Relativistic Quantum Mechanics, Atomic and Nuclear (year 2/3)

Books:
B R Martin and G Shaw, “Particle Physics”, J. Wiley
Halzen and Martin, “Quarks and Leptons”, J. Wiley
D H Perkins, “Introduction to High Energy Physics”, Addison-Wesley.

Assessment:
Examination of 2½ hours duration contributing 90%, coursework 10%.

33
 4450 Particle Accelerator Physics

 Introduction: history of accelerators, basic principles including centre of mass

energy, luminosity, accelerating gradient.

 Characteristics of modern colliders; LEP, LHC, b-factories.

 Transverse motion, principles of beam cooling.

 Strong focusing, simple lattices.

 Circulating beams, synchrotron radiation.

 Longitudinal dynamics.

 Multipoles, non-linearities and resonances.

 Radio Frequency cavities, superconductivity in accelerators.

 Applications of accelerators; light sources, medical uses.

 Future: ILC, neutrino factories, muon collider, laser plasma acceleration.

Books
E. Wilson, An Introduction to Particle Accelerators OUP
S.Y. Lee Accelerator Physics World Scientific (2nd Edition).

Assessment
Written examination of 2½ hours contributing 90%, coursework contributing 10%.

Prerequisites
Second year level electromagnetism.

34
 4472 Order and Excitations in Condensed Matter

Syllabus
The allocation of topics to sessions is shown below. Each session is approximately
three lectures.

Atomic Scale Structure of Material (session 1): The rich spectrum of condensed
matter; Energy and time scales in condensed matter systems; Crystalline materials:
crystal structure as the convolution of lattice and basis; Formal introduction to
reciprocal space.
.
Magnetism: Moments, Environments and Interactions (session 2) Magnetic
moments and angular momentum; diamagnetism and paramagnetism; Hund's rule;
Crystal fields; Exchange interactions

Order and Magnetic Structure (session 3) Weiss model of ferromagnetism and

antiferromagnetism; Ferrimagnetism; Helical order; Spin Glasses; Magnetism in
Metals; Spin-density waves; Kondo effect

Scattering Theory (sessions 4 and 5) X-ray scattering from a free electron (Thomson
scattering); Atomic form factors; Scattering from a crystal lattice, Laue Condition and
unit cell struture factors; Ewald construction; Dispersion corrections; QM derivation
of cross-section; Neutron scattering lengths; Coherent and incoherent scattering

Excitations of Crystalline Materials (session 6) Dispersion curves of 1D monoatomic

chain (revision); Understanding of dispersion curves in 3D materials; Examples of
force constants in FCC and BCC lattices; Dispersion of 1D diatomic chain; Acoustic
and Optic modes in real 3D systems; Phonons and second quantization; Anharmonic
interactions

Magnetic Excitations (session 7) Excitations in ferromagnets and antiferromagnets;

Magnons; Bloch T3/2 law; Excitations in 1, 2 and 3 dimension; Quantum phase
transitions

Sources of X-rays and Neutrons (session 8) Full day visit to RAL. Neutron Sources
and Instrumentation. Synchrotron Radiation. Applications of Synchrotron Radiation

Modern Spectroscopic Techniques (session 9)

Neutron scattering: triple-axis spectrometer, time-of-flight, polarized neutrons
X-ray scattering: X-ray magnetic circular dichroism, resonant magnetic scattering,
reflectivity

Phase transitions and Critical Phenomena (session 10) Broken symmetry and order
parameters in condensed matter. Landau theory and its application to structural phase
transitions, ferromagnetism, etc. Ising and Heisenberg models. Critical exponents.
Universality and scaling

35
Local Order in Liquids and Amorphous Solids (session 11) Structure of simple
liquids; Radial distribution function; Dynamics: viscosity, diffusion; Modelling; Glass
formation; Simple and complex glasses; Quasi-crystals

Textbooks
Main texts: Structure and Dynamics: An Atomic View of Materials, Martin T. Dove
(OUP); Magnetism in Condensed Matter, Stephen Blundell (OUP)
Additional texts: Elements of Modern X-ray Physics, Jens Als-Nielsen and Des
McMorrow (Wiley); Introduction to the Theory of Thermal Neutron Scattering, G.L.
Squires (Dover)

Assessment
Examination of 2½ hours duration contributing 90%, coursework 10%.

Prerequisites
UCL’s PHYS3C25 – Solid State Physics, or an equivalent from another department

36
 4473 Theoretical Treatments of Nano-systems

Overall aim of the course:

An increasing amount of science and technology is nowadays concerned with
processes at the nanometer scale, typically involving functionalized structures like
particles and molecules. Time scales of picoseconds are the natural ones to describe
the vibrational/conformational properties of these systems, and the relevant steps of
their synthesis/assembly mechanisms. Such a high time/size resolution poses
extremely demanding constraints to experimental techniques.

A detailed theoretical description and quantum-based numerical modelling have thus

become indispensable tools in modern research on this systems, as guides for
interpreting the experimental observations and, increasingly, as independent
complementary investigation tools, capable of quantitative predictions. The relevant
physics at the nanoscale is quantum mechanics, and quantum approaches must be
used to provide the potential energy surfaces and the structural/configurational
properties which are at the basis of classical molecular dynamics techniques and
phase-space descriptions.

This course provides an introduction to the rapidly growing area of atomistic-based

theoretical modelling in nano-science, based on fundamental quantum theory. The
course introduces the physics of many-electron systems with a particular focus on
symmetry properties and on the simplifying assumptions which must be used to
successfully model functional nanosized systems. While a main goal of the course is
to provide a theoretical background on the structure and quantum behaviour of matter
at the nano-scale, examples of applications given during the course involve modern
concepts on the nano-scale behaviour of functional materials, and provide an
accessible introduction to some of the main theoretical techniques used to model
processes involving surfaces, interfaces, clusters, and macromolecules.

Objectives:
On successfully completing this course, a student should:
 Be familiar with the fact that the physical properties of complex nano-systems
can be described within a coherent quantum mechanical framework, in
particular that the many-electron QM problem can be attacked by mean-field
techniques of different levels of complexity

 Understand how this theoretical description can be used as a basis for

modelling tools yielding accurate quantum-based potential energy surfaces
and inter-atomic force models, and thus is capable of quantitative predictions
at the nanometer/picosecond size- and time- scales.

Topics:
(1) Foundations: mean-field modelling of many electron systems.
The many-body problem: the general Schroedinger equation problem. The particle
exchange operator, symmetry of a two-body wave function with spin. Wavefunction
classes constructed from spin orbitals. Reminder of perturbation theory.

37
Reminder of variational techniques. Example: the virial theorem for Coulombic
systems. Variational minimum obtained through self-consistency: derivation of a
simple self-consistent Hartree equation for the Helium ground state. Correlation
energy. Many electrons: symmetry of the many body wave function under particle
exchange. Pauli principle and Slater determinants. The general Hartree-Fock method
(outline), electronic correlation in many electron systems. Modern self-consistent
approaches: elements of Density Functional Theory.

(2) Potential energy surfaces and molecular dynamics.

Quantum molecules: the hamiltonian operator, the Born-Oppenheimer approximation,
degrees of freedom of the electronic energy, reminder of the molecular roto-vibration
spectrum. The Hellman-Feynman theorem and the concept of classical interatomic
force-field. The Verlet Algorithm and First-Principles Molecular Dynamics. Classical
potentials, the problem of transferability.

Modelling free energy barriers via thermodynamic integration. Classical dynamics

and stochastic processes. Modelling the diffusion of point defects in crystalline solids.
The central limit theorem and the evolution of a distribution function. The diffusion
coefficient. Derivation of Fick’s laws. Examples and exercises.

(3) Electronic structure, symmetry, case studies.

Approximate representations for the electronic structure of large molecular systems,
derivation of a simple tight-binding scheme (LCAO in the nearest neighbour
approximation). The case of aromatic n-rings: model energy multiplets in aromatic
systems: HOMO and LUMO levels and the prediction of STM images in
negative/positive bias.

The connection between finite and infinite systems: the infinite 1D periodic solid and
direct calculation of a model band structure. Bloch states, the Bloch theorem in Born-
Von Karman periodic conditions. Other notable symmetries.

If time allows, case study (updated each year), e.g. self-assembly of 2D

nanostructures. Construction of a classical force-field and molecular dynamics.

Reading List
1. B. H. Bransden and C. J. Joachain, “Physics of Atoms and Molecules”, Prentice
Hall (2002) ISBN: 058235692X
2. M. Finnis, “Interatomic Forces in Condensed Matter”, Oxford University Press
(2003) ISBN: 0198509774
3. M. P. Allen and D. J. Tildesley, “Computer Simulations of Liquids”, Clarendon
Press (1989) ISBN: 0198556454
4. D. Frenkel and B. Smit, “Understanding Molecular Simulations”, Academic Press
(2001) ISBN: 0122673514

Assessment:
One three-hour examination contributing 100% of the total marks.

Pre-requisites:
CP3221 Spectroscopy and Quantum Mechanics, or equivalent

38
 4475 Physics at the Nanoscale

Overall aim of the course:

Today an increasing amount of science and technology is concerned with processes at
the nano-scale, typified by structures of the order of 10-1000 nanometre in dimension.
At this scale, physics is determined by quantum processes. This course provides an
introduction to the rapidly growing area of nano-science. Already, nano-structures are
“familiar” to us in the structure of the current generation of computer chips, and the
applications of nano-structures are predicted to contribute to the new technologies of
this century. The course introduces the physics and technology of nano-structures,
discusses their special properties, methods of fabricating them, and some of the
methods of analysing them.

Objectives:
On successfully completing this course, a student should:
 Appreciate the difference between the physics on the classical (macro-) scale
and on the quantum (nano-) scale.
 Understand the properties of nanostructures in ‘zero’, one and two dimensions.
 Understand the fabrication and characterisation of nano-devices.

Topics:

Miniaturisation, Moore’s law, electronics, microelectronics, nanoelectronics.

Single electronics.
Coulomb blockade. Single Electron Transistor (SET). Applications of SET.
Cooper-pair box.
Overview of key electron transport properties of metals / semiconductors:
Electron energy spectrum, energy bands, density of electron states. Effective
mass. Fermi surface. Landau quantization and the role of electron scattering,
Dingle temperature. De Haas-van Alphen and Shubnikov-de Haas effects.
Quantum interference of conduction electrons.
Weak localisation, spin-orbit scattering and anti-localisation. Aharonov-Bohm
effect. Mesoscopic regime. h/e and h/2e quantum oscillations. Universal
conductance fluctuations.
Josephson effect in superconductors and Josephson quantum bits.
Flux and phase qubits. Read-out using Superconducting Quantum Interference
Devices (SQUIDs) and Hybrid nano-interferometers.
Semiconductor nano-science
Electrons in a two-dimensional layer:
Density of electron states in low dimensional conductors. GaAs/AlGaAs
structures. Quantum Hall effect.
Electrons in a one-dimensional system: formation in GaAs/AlGaAs.
Density of states. Diffusive and ballistic conduction. Quantised conduction.
Electrons in a zero-dimensional system: Quantum dots
Carbon nanoelectronics.
Carbon nanotubes. Graphene.

39
‘Top down’ fabrication:
PVD thin layer deposition techniques by thermal and e-beam evaporation,
laser ablation. Chemical vapour deposition (CVD) and MOCVD, plasma-
assisted deposition, ion-implanted layers, epitaxial processes.

Nano-lithography:
Resolution limits. Electron-beam lithography. Proximity effect. Negative and
positive lithographic processes. Electron beam resists. Ion beam etching and
RIBE. Plasma-assisted etching. Alignment and self-alignment, Dolan
technique. Focussed ion beam (FIB) nanotechnology, ion-beam lithography.
Nano-analysis:
SEM- and STEM-based methods. X-ray and electron spectroscopy.
Scanning tunneling microscopy. Atomic force microscopy and other scanning
probe-based methods, including scanning near field optical microscopy.
‘Bottom up’ fabrication:
Scanning probe based nano-technology, molecular manufacturing.
Self-organised nano-structures.
Clean-room environment.

Books/references
Marc J. Madou, Fundamentals of Microfabrication, The Science of Miniaturization,
2nd ed, CRC Press, LLC (2002).
S. Washburn and R. A. Webb, Quantum transport in small disordered samples from
the diffusive to the ballistic regime, Rep. Prog. Phys. 55, 1311-1383 (1992).
Michel Devoret and Christian Glattli, Single-electron transistors, Phys. World. Sep 1,
1998.

Assessment:
Examination of 2½ hours duration contributing 90%, coursework 10%.

Pre-requisites:
Quantum mechanics and Condensed matter physics at a typical second year level is
essential. Condensed matter physics at a typical third year level is desirable but not
essential.

40
 4478 Superfluids, Condensates and Superconductors
This course will not be available this session

The extraordinary properties of Superfluids, Superconductors and Bose-Einstein

condensates are fascinating manifestations of macroscopic quantum coherence: the
fact that the low temperature ordered state is described by a macroscopic
wavefunction.

We will study quantum fluids, the superfluidity of liquid 4He and liquid 3He, Bose-
Einstein Condensation in dilute gases, metallic superconductivity, as well as the
different techniques for achieving low temperatures. It is hoped to emphasize the
conceptual links between these very different physical systems. Important
developments in this subject were recognised by Nobel prizes in 2003, 2001, 1997,
1996, 1987, 1978, 1973, 1972, 1962 and 1913, which is one measure of its central
importance in physics.

Introduction and review of quantum statistics.

The statistical physics of ideal Bose and Fermi gases.
Superfluid 4He and Bose-Einstein condensation.
Phase diagram. Properties of superfluid 4He. Bose-Einstein condensation in 4He.
The two-fluid model and superfluid hydrodynamics. Elementary excitations of
superfluid 4He. Breakdown of superfluidity. Superfluid order parameter: the
macroscopic wavefunction. Quantization of circulation and quantized vortices.
Rotating helium.
Bose-Einstein condensation in ultra-cold atomic gases
Cooling and trapping of dilute atomic gases. BEC. Interactions. Macroscopic quantum
coherence. Rotating condensates and vortex lattices. The atom laser.
Liquid 3He; the normal Fermi liquid.
Phase diagram. Properties of normal 3He. Quasiparticles. Landau theory of
interacting fermions.
Liquid solutions of 3He and 4He.
Isotopic phase separation. Spin polarised 3He.
The properties of quantum fluids in two dimensions
Two dimensional Fermi systems. The superfluidity of 2D 4He; the Kosterlitz-
Thouless transition.
Achieving low temperatures
3
He-4He dilution refrigerator. Adiabatic demagnetisation of paramagnetic salts.
Nuclear adiabatic demagnetisation. Pomeranchuk cooling.
Measurement of low temperatures
Thermal contact and thermometry at tremperatures below 1K.
Superfluid 3He.
Superfluid 3He as a model p-wave superfluid. Discovery and identification of the
superfluid ground states. 3He-A, the anisotropic superfluid.
Superconductivity
Review of the basic properties of superconductors. Meissner effect. Type I and type II
superconductors. Pairing in conventional and unconventional superconductors.
Survey of recent advances in novel superconductors.
The Josephson effects.
Josephson effects in superconductors, superfluid 4He and superfluid 3He.

41
Prerequisites:
This course requires knowledge of base level thermodynamics and statistical physics
at year 2/3 level and quantum mechanics at typical year 2 level. A background in
solid state physics and superconductivity as covered in a typical year 3 condensed
matter course is desirable but not essential.

Books:
Course notes, popular articles, scientific articles and review articles, web based
material.
J F Annett, Superconductivity, Superfluids and Condensates, Oxford University Press
(2004)
Tony Guénault, Basic Superfluids, Taylor and Francis (2003)
D R Tilley and J Tilley, Superfluidity and Superconductivity Adam Hilger.
P McClintock, D J Meredith and J K Wigmore, Matter at Low Temperatures 1984,
Blackie. (Out of print).
J Wilks and D S Betts, An Introduction to Liquid Helium 1987, Oxford (out of print).

Assessment:
Written examination of 2½ hours contributing 80%, coursework and essays
contributing 20%.

42
 4501 Standard Model Physics and Beyond

Aims and Objectives:

To introduce the student to the Standard Model of Particle Physics, and its minimal
supersymmetric extensions. In particular the course will discuss the constituents of the
Standard Model and the underlying Lie group structure, within the framework of
gauge invariant quantum field theory, which will be introduced to the student in
detail, discuss the physical mechanism for mass generation (Higgs), consistently with
gauge invariance, and finally present an introduction to (minimal) Supersymmetric
Extensions of the Standard Model. In the latter respect, we shall also discuss
implications of supersymmetry for astroparticle physics issues, in particular dark
matter (provided by the supersymmetric partners) and how astrophysical observations
can constrain such particle physics models.

Prerequisites
Level 2/3 nuclear physics
4242 Relativistic Waves and Quantum Fields or equivalent
4205 Lie Groups and Lie Algebras. or equivalent
Familiarity with tensors, e.g a General Relativity course, is highly desirable.

43
 4512 Nuclear Magnetic Resonance
Course taught at RHUL – Egham campus and available over VideoCon at QMUL

This course will introduce students to the principles and methods of nuclear magnetic
resonance. It will apply previously learned concepts to magnetic resonance. Students
should appreciate the power and versatility of this technique in a variety of
applications.

 Introduction: static and dynamic aspects of magnetism, Larmor precession,

relaxation to equilibrium, T1 and T2, Bloch equations.

 Pulse and continuous wave methods: time and frequency domains.

Manipulation and observation of magnetisation, 90º and 180º pulses, free
induction decay.

 Experimental methods of pulse and CW NMR: the spectrometer, magnet.

Detection of NMR using SQUIDs.

 Theory of relaxation: transverse relaxation of stationary spins, the effect of

motion. Spin lattice relaxation.

 Spin echoes: ‘violation’ of the Second Law of Thermodynamics, recovery of

lost magnetisation. Application to the measurement of T2 and diffusion.

 Analytical NMR: chemical shifts, metals, NQR.

 NMR imaging: Imaging methods. Fourier reconstruction techniques. Gradient

echoes. Imaging other parameters.

Books: B P Cowan, Nuclear Magnetic Resonance and Relaxation, CUP, 1st ed. 1997
and 2nd ed. 2005.
Journal and web references given during course.

Prerequisites: 2nd year-level electromagnetism and quantum mechanics

Assessment:
Written examination of 2½ hours contributing 90%, coursework contributing 10%.

44
 4515 Computing and Statistical Data Analysis

This course aims to introduce students to programming techniques using the C++
language on a Unix platform. It will also introduce students to techniques of
probability and statistical data analysis and they will study applications of data
analysis using C++ based computing tools.

 Introduction to C++ and the Unix operating system.

 Variables, types and expressions.
 Functions and the basics of procedural programming.
 I/O and files.
 Basic control structures: branches and loops.
 Arrays, strings, pointers.
 Basic concepts of object oriented programming.
 Probability: definition and interpretation, random variables, probability
density functions, expectation values, transformation of variables, error
propagation, examples of probability functions.
 The Monte Carlo method: random number generators, transformation method,
acceptance-rejection method.
 Statistical tests: significance and power, choice of critical region, goodness-of-
fit.
 Parameter estimation: samples, estimators, bias, method of maximum
likelihood, method of least squares, interval estimation, setting limits,
unfolding.

Books: R. Miller, An Introduction to the Imperative Part of C++,

www.doc.ic.ac.uk/~wjk/C++Intro.
W. Savitch, Problem Solving with C++: The Object of Programming, 4th
Ed., Addison-Wesley, 2003.
G D Cowan, Statistical Data Analysis, Clarendon Press, 1998.
R J Barlow, Statistics: A Guide to the Use of Statistical Methods in the
Physical Sciences, John Wiley, 1989.

Prerequisites: none

Assessment:
Written examination of 2½ hours contributing 70%, coursework contributing 30%.

45
 4534 String Theory and Branes

Aims and Objectives:

The main aim of the course is to give a first introduction to string theory which
can be used as a basis for undertaking research in this and related subjects.

Syllabus:
Topics will include the following: classical and quantum dynamics of the point
particle, classical and quantum dynamics of strings in spacetime, D-branes, the
spacetime effective action, and compactification of higher dimensions.

Web page: http://www.mth.kcl.ac.uk/courses-10-11/

Teaching Arrangements:
Two hours of lectures each week

Prerequisites:
Note – A high level of mathematical ability is required for this course
The course assumes that the students have an understanding of special relativity
and quantum field theory. In addition the student should be familiar with General
Relativity, or be taking the Advanced General Relativity course concurrently.
4205 Lie Groups and Lie Algebras would be helpful

Assessment:
The course will be assessed by a two-hour written examination at the end of the
academic year.

Assignments:
During the lectures problems will be given and complete solutions will be made
available. It is crucial that students work through these problems on their own.

Reading List:
The lecture notes taken during the lectures are the main source. However, some
of the material is covered in:
 Green, Schwarz and Witten: String Theory 1, Cambridge University Press.
 B. Zwiebach: A First Course in String Theory, Cambridge University Press.

46
 4541 Supersymmetry and Gauge Symmetry

Aims and objectives:

This course aims to provide an introduction to two of the most important concepts
in modern theoretical particle physics; gauge theory, which forms the basis of the
Standard Model, and supersymmetry. While gauge theory is known to play a
central role in Nature, supersymmetry has not yet been observed but
nevertheless forms a central pillar in modern theoretical physics.

Syllabus:
Maxwell’s equations as a gauge theory. Yang-Mills theories. Supersymmetry.
Vacuum moduli spaces, extended supersymmertry and BPS monopoles.

Web page: http://www.mth.kcl.ac.uk/courses-10-11/

Teaching arrangements:
Two hours of lectures each week

Prerequisites:
Note – A high level of mathematical ability is required for this course
Students should be familiar with quantum field theory, special relativity as well as
an elementary knowledge of Lie algebras.

Assessment:
The courses will be assessed by a two hour written examination at the end of the
academic year.

Assignments:
During the lectures problems will be given and complete solutions will be made
available. It is crucial that students work through these problems on their own.

Books:
The lecture notes taken during the lectures are the main source but see also
 D. Bailin and A. Love: Supersymmetric Gauge Field Theory and String
Theory, Taylor and Francis.
 L. Ryder: Quantum Field Theory, Cambridge University Press
 P. West: Introduction to Supersymmetry, World Scientific

47
 4600 Stellar Structure and Evolution

Course outline
Stars are important constituents of the universe. This course starts from well known
physical phenomena such as gravity, mass conservation, pressure balance, radiative
transfer of energy and energy generation from the conversion of hydrogen to helium.
From these, it deduces stellar properties that can be observed (that is, luminosity and
effective temperature or their equivalents such as magnitude and colour) and
compares the theoretical with the actual. In general good agreement is obtained but
with a few discrepancies so that for a few classes of stars, other physical effects such
as convection, gravitational energy generation and degeneracy pressure have to be
included. This allows an understanding of pre-main sequence and dwarf stages of
evolution of stars, as well as the helium flash and supernova stages.

Syllabus – Topics covered include:

 Observational properties of stars, the H-R diagram, the main sequence, giants
and white dwarfs.

 Properties of stellar interiors: radiative transfer, equation of state, nuclear

reactions, convection.

 Models of main sequence stars with low, moderate and high mass.

 Pre- and post-main sequence evolution, models of red giants, and the end state
of stars.

The course includes some exposure to simple numerical techniques of stellar structure
and evolution; computer codes in Fortran.

Prerequisites: some knowledge of Fluids, Electromagnetism, Stellar Structure

Books: Course Notes available + R Kippenhahn and A Weigert - Stellar Structure and
Evolution Springer

Assessment: Written examination of 3 hours contributing 100%

48
 4601 Advanced Cosmology

Course outline
Cosmology is a rapidly developing subject that is the focus of a considerable research
effort worldwide. It is the attempt to understand the present state of the universe as a
whole and thereby shed light on its origin and ultimate fate. Why is the universe
structured today in the way that it is, how did it develop into its current form and what
will happen to it in the future? The aim of this course is to address these and related
questions from both the observational and theoretical perspectives. The course does
not require specialist astronomical knowledge and does not assume any prior
understanding of general relativity.

Syllabus
 Observational basis for cosmological theories.

 Derivation of the Friedmann models and their properties.

 Cosmological tests; the Hubble constant; the age of the universe; the density
parameter; luminosity distance and redshift.

 The cosmological constant.

 Physics of the early universe; primordial nucleosynthesis; the cosmic

microwave background (CMB); the decoupling era; problems of the Big Bang
model.

 Inflationary cosmology.

 Galaxy formation and the growth of fluctuations

 Evidence for dark matter.

 Large and small scale anisotropy in the CMB.

Prerequisites: Knowledge of Newtonian Dynamics and Gravitation, and Calculus.

Books:

Assessment: Written examination of 3 hours contributing 100%

49
 4602 Relativity and Gravitation

 Introduction to General Relativity.

 Derivation from the basic principles of Schwarzschild.

 Solution of Einstein's field equations.

 Reisner-Nordstrom, Kerr and Kerr-Neuman solutions and physical aspects of

strong gravitational fields around black holes.

 Generation, propagation and detection of gravitational waves.

 Weak general relativistic effects in the Solar System and binary pulsars.

 Alternative theories of gravity and experimental tests of General Relativity.

Prerequisites: knowledge of Relativity

Books:

Assessment: Written examination of 3 hours contributing 100%.

50
 4604 General Relativity and Cosmology

Syllabus outline
Mathematical tools for handling curved space. Metric. Geodesics. Principle of
equivalence, experimental confirmations. Cosmology, Robertson-Walker solution, the
Big Bang. Einstein’s field equations, Schwarzchild solution, observed effects, black
holes.

Aims and Objectives

The aim of this optional course is to provide a first treatise on general relativity and
cosmology, as a prerequisite for those students who would like to continue further
studies in mathematical or theoretical particle physics. The structure of the course is
aimed at the mathematically advanced students, and skills in mathematics are
essential, given that a substantial part of the course deals with tensors and other
advanced mathematical concepts, such as elements of differential geometry. Some
techniques used in this course, such as Lagrange equations, are also taught in greater
detail in other third year courses, such as mathematical methods.

51
 4605 Astroparticle Cosmology
Syllabus outline
The module will focus on cosmology and gravitational and high energy physics in the
context of early universe. Students will study and gain an understanding of Einstein's
field equations and gravitational dynamics; homogeneous isotropic spaces;
anisotropic and inhomogeneous spaces; physics of the very early universe; the Planck
era.

Aims and Objectives

Students completing this module will have a deep and systematic understanding of
knowledge in cosmological principles in the early universe and can work with
theoretical knowledge like Einstein's field equations. A comprehensive understanding
of Newtonian theory, General Relativity and other specialised methodologies.
Students will develop critical awareness can undertake analysis of complex areas of
knowledge communicating the outcome effectively. A level of conceptual
understanding that will allow her/him critically to evaluate research, advanced
scholarship and methodologies and argue alternative approaches

A student will be able to competently undertake research tasks with minimum

guidance.

The successful student on this module will have an independent learning ability
required for continuing professional study.

52
 4630 Planetary Atmospheres

Comparison of the Planetary Atmospheres (2 lectures)

The radiative energy balance of a planetary atmosphere; the competition between
gravitational attraction and thermal escape processes. The factors which influence
planetary atmospheres; energy and momentum sources; accretion and generation of
gases; loss processes; dynamics; composition.
Atmospheric structure (7 lectures)
Hydrostatic equilibrium, adiabatic lapse rate, convective stability, radiative transfer,
the greenhouse effect and the terrestrial planets.
Oxygen chemistry (3 lectures)
Ozone production by Chapman theory; comparison with observations; ozone
depletion and the Antarctic ozone hole.
Atmospheric temperature profiles (3 lectures)
Troposphere, stratosphere, mesosphere, thermosphere and ionosphere described; use
of temperature profiles to deduce energy balance; internal energy sources; techniques
of measurement for remote planets.
Origin of planetary atmospheres and their subsequent evolution (3 lectures)
Formation of the planets; primeval atmospheres; generation of volatile material;
evolutionary processes; use of isotopic abundances in deducing evolutionary effects;
role of the biomass at Earth; consideration of the terrestrial planets and the outer
planets.
Atmospheric Dynamics (4 lectures)
Equations of motion; geostrophic and cyclostrophic circulation, storms; gradient and
thermal winds; dynamics of the atmospheres of the planets; Martian dust storms, the
Great Red Spot at Jupiter.
Magnetospheric Effects (1 lecture)
Ionisation and recombination processes; interaction of the solar wind with planets and
atmospheres; auroral energy input.
Atmospheric loss mechanisms (1 lecture)
Exosphere and Jeans escape; non thermal escape processes; solar wind scavenging at
Mars.
Observational techniques (3 lectures)
Occultation methods from ultraviolet to radiofrequencies; limb observation
techniques; in-situ probes.
Global warming (3 lectures)
Recent trends and the influence of human activity; carbon budget for the Earth;
positive and negative feedback effects; climate history; the Gaia hypothesis;
terraforming Mars.

Books:
J. W. Chamberlain and D. M. Hunten, “Theory of Planetary Atmospheres” Academic
Press.
M. Salby, “Introduction to Atmospheric Physics”, Academic Press.
J. T. Houghton, “The Physics of Atmospheres”, Cambridge University Press.

Assessment:
Examination of 2½ hours duration contributing 90%, coursework 10%.

53
 4640 Solar Physics

1. Introduction
Presentation of the syllabus and suggested reading, a list of solar parameters and a
summary of the topics to be treated during the course. (1)

2. The Solar Interior and Photosphere

Stellar Structure and Evolution. Life history of a star. Equations and results.
Conditions for Convection. Arrival of the Sun on the Main Sequence. Nuclear fusion
reactions. The Standard Solar Model. Neutrino production and Detection – the
neutrino problem. Solar Rotation. Photospheric models and observations. Fraunhofer
lines. Chemical composition. Convection and Granulation. Waves and oscillations –
Helioseismology or probing the SunUs interior. (12)

3. Solar Magnetic Fields/Solar Activity

Sunspot observations – structure, birth and evolution. Spot temperatures and
dynamics. Observations of faculae. Solar magnetism – Sunspot and Photospheric
fields. Active Region manifestations and evolution. Solar Magnetic Cycle –
Observations and Dynamics. Babcock dynamo model of the solar cycle. Behaviour of
flux tubes. Time behaviour of the Sun’s magnetic field. (4)

4. The Solar Atmosphere - Chromosphere

Appearance of the Chromosphere – Spicules, mottles and the network. Observed
spectrum lines. Element abundances. Temperature profile and energy flux. Models of
the Chromosphere. Nature of the Chromosphere and possible heating mechanisms. (4)

5. The Solar Atmosphere - Corona and Solar Wind

Nature and appearance of the corona. Breakdown of LTE. Ionization/ recombination
balance and atomic processes. Spectroscopic observations and emission line
intensities. Plasma diagnostics using X-ray emission lines. Radio emission. Summary
of coronal properties. Discovery of the solar wind. X-ray emission and coronal holes.
In-situ measurements and the interplanetary magnetic field structure. Solar wind
dynamics. Outline of the Heliosphere. (6)

6. Solar Flares.
Flare observations throughout the solar atmosphere. Thermal and non-thermal
phenomena. Particle acceleration and energy transport. Gamma-ray production. Flare
models and the role of magnetic fields. (3)

Assessment:
Examination of 2½ hours duration contributing 90%, coursework 10%.

54
 4650 Solar System
Course outline
As the planetary system most familiar to us, the Solar System presents the best
opportunity to study questions about the origin of life and how enormous complexity
arise from simple physical systems in general. This course surveys the physical and
dynamical properties of the Solar System. It focuses on the formation, evolution,
structure, and interaction of the Sun, planets, satellites, rings, asteroids, and comets.
The course applies basic physical and mathematical principles needed for the study,
such as fluid dynamics, electrodynamics, orbital dynamics, solid mechanics, and
elementary differential equations. However, prior knowledge in these topics is not
needed, as they will be introduced as required. The course will also include
discussions of very recent, exciting developments in the formation of planetary and
satellite systems and extrasolar planets (planetary migration, giant impacts, and
exoplanetary atmospheres).

Syllabus
 General overview/survey.

 Fundamentals: 2-body problem, continuum equations.

 Terrestrial planets: interiors, atmospheres.

 Giant planets: interiors, atmospheres.

 Satellites: 3-body problem, tides.

 Resonances and rings.

 Solar nebula and planet formation.

 Asteroids, comets and impacts.

Assessment: Written examination of 3 hours contributing 100%

Book: C.D. Murray and S.F. Dermott, Solar System Dynamics, Cambridge
University
Press.

55
 4660 The Galaxy

Course outline
The course considers in detail the basic physical processes that operate in galaxies,
using our own Galaxy as a detailed example. This includes the dynamics and
interactions of stars, and how their motions can be described mathematically. The
interstellar medium is described and models are used to represent how the abundances
of chemical elements have changed during the lifetime of the Galaxy. Dark matter can
be studied using rotation curves of galaxies, and through the way that gravitational
lensing by dark matter affects light. The various topics are then put together to
provide an understanding of how the galaxies formed.

Syllabus
 Introduction: galaxy types, descriptive formation and dynamics.

 Stellar dynamics: virial theorem, dynamical and relaxation times, collisionless

Boltzmann equation, orbits, simple distribution functions, Jeans equations.

 The interstellar medium: emission processes from gas and dust (qualitative
only), models for chemical enrichment.

 Dark matter - rotation curves: bulge, disk, and halo contributions.

 Dark matter - gravitational lensing: basic lensing theory, microlensing optical

depth.

 The Milky Way: mass via the timing argument, solar neighbourhood
kinematics, the bulge, the Sgr dwarf.

Assessment: Written examination of 3 hours contributing 100%

References: Shu for some basic material, Binney & Merrifield and Binney &
Tremaine for some topics, plus full course notes.

56
 4670 Astrophysical Plasmas

 The plasma state as found in astrophysical contexts.

 Particle motion in electromagnetic fields, cyclotron motion, drifts and

mirroring, with application to the radiation belts and emission from radio
galaxies.

 Concepts of magnetohydrodynamics (MHD); flux freezing and instabilities.

 The solar wind, including MHD aspects, effects of solar activity, and impact
on the terrestrial environment.

 Magnetic reconnection; models and application to planetary magnetic storms

and stellar flares and coronal heating.

 Shock waves and charged particle acceleration.

Assessment: Examination of 2½ hours duration contributing 90%, coursework 10%.

57
 4680 Space Plasma and Magnetospheric Physics
Introduction [1]
Plasmas in the solar system, solar effects on Earth, historical context of the
development of this rapidly developing field
Plasmas [3]
What is a plasma, and what is special about space plasmas; Debye shielding,
introduction to different theoretical methods of describing plasmas
Single Particle Theory [6]
Particle motion in various electric and magnetic field configurations; magnetic
mirrors; adiabatic invariants; particle energisation
Earth’s Radiation Belts [3]
Observed particle populations; bounce motion, drift motion; South Atlantic Anomaly;
drift shell splitting; source and acceleration of radiation belt particles; transport and
loss of radiation belt particles
Introduction to Magnetohydrodynamics [3]
Limits of applicability; convective derivative; pressure tensor; continuity equation;
charge conservation and field aligned currents; equation of motion; generalised
Ohm’s law; frozen-in flow; magnetic diffusion; equation of state; fluid drifts;
magnetic pressure and tension
The Solar Wind [3]
Introduction, including concept of heliosphere; fluid model of the solar wind (Parker);
interplanetary magnetic field and sector structure; fast and slow solar wind; solar wind
at Earth; coronal mass ejections
The Solar Wind Interaction with Unmagnetised Bodies [2]
The Moon; Venus, Comets
The Solar Wind and Magnetised Bodies (I) [4]
Closed Magnetosphere Model
The ring current, boundary currents; shape of the magnetopause; corotation;
convection driven by viscous flow
The Solar Wind and Magnetised Bodies (II) [3]
Open Magnetosphere Model, Steady State
Magnetic reconnection; steady state convection; currents and potentials in an open
magnetosphere; the magnetotail; the plasmasphere; the aurorae
The Solar Wind and Magnetised Bodies (III) [2]
Open Magnetosphere Model, Non-Steady State
Phases of a substorm; Substorm current systems and unanswered questions about
substorms; magnetic storms; dayside reconnection.

Books: M.Kivelson and C.T.Russell, Introduction to space physics, Cambridge

University Press, W.Baumjohann and R.Treumann, Basic space plasma physics,
Imperial College Press

Assessment: Written Examination, 2½ hours, contributing 90%, coursework 10%.

Prerequisites: While the course is essentially self-contained, some knowledge of

basic electromagnetism and mathematical methods is required. In particular it is
assumed that the students are familiar with Maxwell’s equations and related vector
algebra.

58
 4690 Extrasolar Planets and Astrophysical Discs

Course outline
Ever since the dawn of civilisation, human beings have speculated about the existence
of planets outside of the Solar System orbiting other stars. The first bona fide
extrasolar planet orbiting an ordinary main sequence star was discovered in 1995, and
subsequent planet searches have uncovered the existence of more than one hundred
planetary systems in the Solar neighbourhood of our galaxy. These discoveries have
reignited speculation and scientific study concerning the possibility of life existing
outside of the Solar System.

This module provides an in-depth description of our current knowledge and

understanding of these extrasolar planets. Their statistical and physical properties are
described and contrasted with the planets in our Solar System. Our understanding of
how planetary systems form in the discs of gas and dust observed to exist around
young stars will be explored, and current scientific ideas about the origin of life will
be discussed. Rotationally supported discs of gas (and dust) are not only important for
explaining the formation of planetary systems, but also play an important role in a
large number of astrophysical phenomena such as Cataclysmic Variables, X-ray
binary systems, and active galactic nuclei. These so-called accretion discs provide the
engine for some of the most energetic phenomena in the universe.

The second half of this module will describe the observational evidence for accretion
discs and current theories for accretion disc evolution.

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 4702 Environmental Remote Sensing

Teaching Assistants: Tom Smith & Jinda Sae-Jung

Module Structure
Lectures every 2 weeks and Practical Classes every 2 weeks.
All are run in the 1st semester at King’s, check the MSci website for details.

Module Outline
Week 1, Lecture 1: Introduction to EMR and Spectroscopy
Week 2, Practical 1: Introduction to Spectral Measurements
Week 3, Lecture 2: Principles of Optical Remote Sensing from Space
Week 4, Practical 2: Introduction to Spectral Datasets, Data Display and ENVI
Week 5, Lecture 3: Multispectral Sensors and Image Classification
Week 6, Practical 3a: Image Calibration, Annotation and Vegetation Indices
Practical 3b: Image Classification and Change Detection
Week 7, Lecture 4: Thermal Remote Sensing
Week 8, Practical 4: Thermal Remote Sensing of Vegetation Fires and Water Surface
Temperatures
Week 9, Lecture 5: Image Processing
Week 10, Practical 5: Image Registration, Overlays and Output

Assessment
This course is assessed via two methods:
(a) 3 x multiple choice online quizzes - each worth 10% (undertaken after Lectures 3,
4 and 5 and covering the previous lecture)
(b) 1 x CW project (3000 words and worth 70%) - due on 27 January 2012.
[In addition there will be two formative (non-assessed) pieces - a "practice" online
quiz and a coursework project proposal]

Books
• Jensen, J. R. Remote Sensing of Environment – An Earth Resource perspective.
(Prentice Hall, 2000).
• Lillesand, T. and Kiefer, R. Remote Sensing and Image Interpretation. (New York:
Wiley, 2007 or earlier edition)

Websites
NASA Remote Sensing Tutorial http://rst.gsfc.nasa.gov/
NASA Earth Observatory http://earthobservatory.nasa.gov

Additional Useful Explanatory Websites

• http://www.astronomynotes.com/light/s1.htm
• http://www.crisp.nus.edu.sg/~research/tutorial/rsmain.htm
• http://landsathandbook.gsfc.nasa.gov/handbook/handbook_site_map.hml
• http://speclab.cr.usgs.gov/PAPERS.refl-mrs/
• http://speclab.cr.usgs.gov/PAPERS/tetracorder/
• http://earthobservatory.nasa.gov/Library/EO1/eo1.html
• http://earthobservatory.nasa.gov/Features/EarthPerspectives/page3.php

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Online Data Sources
• NOAA AVHRR: CLASS internet database
http://www.class.noaa.gov/nsaa/products/welcome
• Landsat/ASTER: ESDI internet site
http://glcfapp.umiacs.umd.edu:8080/esdi/esdi_index.jsp
• Landsat MSS, TM and ETM+: Earth Explorer
http://edcsns17.cr.usgs.gov/EarthExplorer/
• Landsat MSS, TM and ETM+: New Earth Explorer
http://edcsns17.cr.usgs.gov/NewEarthExplorer/
• Landsat MSS, TM and ETM+ (over USA only): GLOVIS: http://glovis.usgs.gov/
• MODIS level 1b: NASA GSFC http://modis.gsfc.nasa.gov/data/
• ASTER L1B (over USA only): GLOVIS: http://glovis.usgs.gov/
• ASTER L1b (elsewhere): Request access for educational use at
https://igskmncnwb001.cr.usgs.gov/aster/afd/index.php

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 4800 Molecular Biophysics

Aims of the Course

The course will provide the students with insights in the physical concepts of some of
the most fascinating processes that have been discovered in the last decades: those
underpinning the molecular machinery of the biological cell. These concepts will be
introduced and illustrated by a wide range of phenomena and processes in the cell,
including biomolecular structure, DNA packing in the genome, molecular motors and
neural signalling.
The aim of the course is therefore to provide students with:
 Knowledge and understanding of physical concepts that are relevant for
understanding biology at the micro- to nano-scale.
 Knowledge and understanding of how these concepts are applied to describe
various processes in the biological cell.

Objectives
 After completing this half-unit course, students should be able to:
 Give a general description of the biological cell and its contents
 Explain the concepts of free energy and Boltzmann distribution and discuss
osmotic pressure, protein structure, ligand-receptor binding and ATP
hydrolysis in terms of these concepts.
 Explain the statistical-mechanical two-state model, describe ligand-receptor
binding and phosphorylation as two-state systems and give examples of
“cooperative” binding.
 Describe how polymer structure can be viewed as the result of random walk,
using the concept of persistence length, and discuss DNA and single-
molecular mechanics in terms of this model
 Explain the worm-like chain model and describe the energetics of DNA
bending and packing; explain how such models are relevant for the rigidity of
cells
 Explain the low Reynolds-number limit of the Navier-Stoke's equation and
discuss its consequences for dynamics in biological systems
 Explain simple solutions of the diffusion equation in biological systems and
their consequences for diffusion and transport in cells
 Explain the concept of rate equations and apply it to step-wise molecular
reactions
 Give an overview of the physical concepts involved in molecular motors and
apply them to obtain a quantitative description of motor driven motion and
force generation
 Describe neural signalling in terms of propagating (Nernst) action potentials
and ion channel kinetics
 Link the material in the course to at least one specific example of research in
the recent scientific literature

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Syllabus
(The approximate allocation of lectures to topics is given in brackets below.)
Biological cells [3]
Introduction to the biology of the cell – cell types – cell components – DNA, RNA,
proteins, lipids, polysaccharides – overview of functional processes in cells
Statistical mechanics in the cell [4]
Deterministic versus thermal forces – free-energy minimisation and entropy,
Boltzmann distribution – free energy of dilute solutions, osmotic pressure/forces –
consequences for protein structure and hydrophobicity – equilibrium constants for
ligand-receptor binding and ATP hydrolysis
Two-state systems [3]
Biomolecules with multiple states – Gibbs distribution – ligand-receptor binding,
phosphorylation – “cooperative” binding
Structure of macromolecules [3]
Random walk models of polymers – entropy, elastic properties and persistence length
of polymers – DNA looping, condensation and melting – single-molecule mechanics
Elastic-rod theory for (biological) macromolecules [3]
Beam deformation and persistence length – worm-like chain model – beam theory
applied to DNA – cytoskeleton
Motion in biological environment [4]
Navier-Stokes equation – viscosity and Reynold's number in cells – diffusion equation
and its solutions – transport and signalling in cells – diffusion limited reactions
Rate equations and dynamics in the cell [3]
Chemical concentrations determine reaction rates – rate equations for step-wise
molecular reactions – Michaelis-Menten kinetics
Molecular motors [4]
Molecular motors in the cell – rectified Brownian motion – diffusion equation for a
molecular motor – energy states and two-state model for molecular motors – force
generation by polymerisation
Action potentials in nerve cells [3]
Nerst potentials for ions – two-state model for ion channels – propagation of action
potentials – channel conductance

Prerequisites
It is recommended but not mandatory that students have taken second level Thermal
Physics. Second level Statistical Thermodynamics would be useful but is not
essential. The required concepts in statistical mechanics will be (re-)introduced during
the course.

Methodology and Assessment

This is a half-unit course, with 30 lectures and 3 discussion/problems classes. Basic
problem-solving skills will be stimulated by the setting of a weekly problem question.
The answers will be collected weekly and more extensively discussed during the
discussion/problem classes. The marks on these problem questions account for 10%
of the overall course assessment. The remaining 90% is determined via an unseen
written examination.

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Textbooks
The course will make extensive use of the following book, parts of which will be
obligatory reading material:

 Physical Biology of the Cell, 1st Edition, R. Phillips, J. Kondev, and J.

Theriot, Garland Science 2009.

Other books which may be useful include the following. They cover more material
than is in the syllabus.

 Biological Physics, 1st Edition, Philip Nelson, W.H. Freeman., 2004.

 Mechanics of Motor Proteins and the Cytoskeleton, 1st Edition, J. Howard,
Sinauer Associates, 2001.
 Protein Physics, 1st Edition, A.V. Finkelstein and O.B. Ptitsyn, Academic
Press, 2002.
 Molecular Driving Forces, 1st Edition, K.A. Dill and S. Bromberg, Garland
Science, 2003.

The following books may be useful for biological reference.

 Molecular Biology of the Cell, 4th Edition, B. Alberts et al., Garland Science,
2002.
 Cell Biology, 2nd Edition, T.D. Pollard, W.C. Earnshaw and J. Lippincott-
Schwartz, Elsevier, 2007.

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 4810 Theory of Complex Networks

Aims and objectives:

The purpose of this module is to provide an appropriate level of understanding of the
mathematical theory of complex networks. It will be explained how complex network
can be quantified and modelled

Syllabus:
This course has four parts
 In part I we focus on the definition and characterization of networks and their
topological features. This includes degrees, degree correlations, loops, and
spectra.
 In part II we study specific ensembles of random networks, and calculate their
properties in the language of part I, such as Erdos-Renyi graphs, small-world
networks, `hidden variable' ensembles, and degree-constrained ensembles.
 Part III is devoted to the connection between network topology and collective
processes defined on such networks. We discuss the different methods
available for studying this link, such equilibrium replica theory, the cavity
method, and (very briefly) generating functional analysis.
 In part IV we briefly discuss algorithms for graph generation like preferential
attachment, hidden variables, and Steger-Wormald algorithms.

Web page: See http://www.mth.kcl.ac.uk/courses-10-11/

Teaching arrangements:
Two hours of lectures per week

Prerequisites:
KCL’s 4CCM111A Calculus I or equivalent
KCL’s 4CCM141A Probability and Statistics I or equivalent

Assessment:
One two-hour written examination at the end of the academic year. 100%

Books:
S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks: From Biological Nets
to the Internet and WWW, Oxford University Press 2003

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 4820 Equilibrium Analysis of Complex Systems

Aims and objectives:

The purpose of this module is to provide an appropriate level of understanding of the
notions and mathematical tools of statistical mechanics of complex and disordered
systems. It will be explained how to use these techniques to investigate complex
physical, biological, economic and financial systems.

Syllabus:
 Canonical ensembles and distributions
 Transfer matrices, asymptotic methods (Laplace and saddle point integration)
approximation methods (mean-field, variational, perturbative)
 Methods for disordered systems (replica, cavity, restricted annealing)
 Application of statistical mechanics to physical and biological systems, to
information processing, optimization, and to models of risk for economic,
financial, and general process-networks.

Web page: See http://www.mth.kcl.ac.uk/courses-10-11/

Teaching arrangements:
Two hours of lectures per week

Prerequisites:
KCL’ s 4CCM111A Calculus I or equivalent
KCL’ s 4CCM112A Calculus II or equivalent
KCL’ s 4CCM141A Probability and Statistics I or equivalent

Assessment:
One two-hour written examination at the end of the academic year. 100%

Books:
L E Reichl, A Modern Course in Statistical Physics, 3rd edition, Wiley VCH (2009)
D J C MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge
Univ Press (2003)
J Voit, The Statistical Mechanics of Financial Markets, Springer Berlin (2001)

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 4830 Dynamical Analysis of Complex Systems

Aims and objectives:

The purpose of this module is to provide an appropriate level of understanding of the
notions and mathematical tools of dynamics of complex systems. It will be explained
how to use these techniques to deeply comprehend dynamical properties of complex
biological and physical systems.

Syllabus:
 Stochastic processes, Markov chains (Chapman-Kolmogorov equation,
irreducibility and aperiodicity, stationary distribution).
 Deterministic processes and Liouville’s equation; Jump processes and Master
equation; Diffusion processes and Fokker-Planck equation.
 Stochastic differential equation, stochastic integration, Langevin equation
 Generating functional analysis formalism
 Application to complex and disordered systems, physical, biological, financial.

Web page: See http://www.mth.kcl.ac.uk/courses-10-11/

Teaching arrangements:
Two hours of lectures per week

Prerequisites:
KCK’s 4CCM111A Calculus I
KCK’s 4CCM112A Calculus II
KCK’s 4CCM141A Probability and Statistics
KCK’s 4CCM131A Introduction to Dynamical Systems
KCK’s 5CCM211A Partial Differential Equations and Complex Variables

Assessment:
One two-hour written examination at the end of the academic year. 100%

Books:
N.G.Van Kampen, Stochastic processes in Physics and Chemistry, Elsevier 3rd
edition 2007
Crispin Gardiner, Stochastic Methods, A handbook for the Natural and Social
Science, Springer 4th edition 2008
Jean Zinn-Justin, Quantum field theory and critical phenomena, Oxford University
Press 4th edition 2002

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 4840 Mathematical Biology

Aims and objectives:

The purpose of this module is to provide an appropriate level of understanding of the
Mathematical Biology. With the advent of computational biology and gene
sequencing projects, mathematical modelling in biology is becoming increasingly
important. The module will introduce mathematical concepts such as a nonlinear
dynamical systems and reaction-diffusion partial differential equations, which will be
applied to biological structures and processes.

Syllabus:
 Continuous and discrete population models for single species
 Models for Interacting Populations - Predator–Prey Models: Lotka–Volterra
Systems, Competition Models.
 Reaction Kinetics – Enzyme Kinetics, the Michaelis–Menten system,
Autocatalysis, Activation and Inhibition.
 Biological Oscillators and Switches – Feedback Control Mechanisms,
Hodgkin–Huxley Theory of Nerve Membranes.
 Belousov–Zhabotinskii Reactions.
 Dynamics of Infectious Diseases – Simple Epidemic Models, Multi-Group
Models.
 Reaction Diffusion, Chemotaxis, and Nonlocal Mechanisms.
 Biological Waves in Single-Species Models

Web page: See http://www.mth.kcl.ac.uk/courses-10-11/

Teaching arrangements:
Two hours of lectures per week

Prerequisites:
KCL’s 4CCM111A Calculus I
KCL’s 4CCM112A Calculus II
KCL’s 4CCM113A Linear Methods
KCL’s 4CCM131A Introduction to Dynamical Systems
KCL’s 5CCM211A Partial Differential Equations and Complex Variables
----or equivalent courses

Assessment:
One two-hour written examination at the end of the academic year. 100%

Books:
J.D. Murray, Mathematical Biology, 3rd Edition Springer 2002

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 4850 Elements of Statistical Learning

Aims and objectives:

The purpose of this module is to provide an appropriate level of understanding of
Statistical Learning presented in the framework of Bayesian Decision theory. It will
be explained how to use linear models for regression and classification as well as
Kernel Methods, graphical models and approximate inference.

Syllabus:
 Introduction
 Probability distributions
 Linear models for regression and classification
 Kernel methods
 Graphical Models
 Approximate Inference

Web page: See http://www.mth.kcl.ac.uk/courses-10-11/

Teaching arrangements:
Two hours of lectures per week

Prerequisites:
KCL’s 4CCM141A Probability and Statistics I or equivalent

Assessment:
One two-hour written examination at the end of the academic year. 100%

Books:
C. Bishop, Pattern Recognition and Machine Learning, Springer 2006
D. Barber, Bayesian Reasoning and Machine Learning, 2009

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