Module Identifier PHM1510
Module Title STATISTICAL PHYSICS
Academic Year 2007/2008
Co-ordinator Professor Keith Birkinshaw
Semester Semester 1
Other staff Professor L Grischuck (Cardiff)
Pre-Requisite Successful Completion of Year 3 of the MPhys Scheme
Course delivery Lecture   20 lectures
Seminars / Tutorials   3 seminars / tutorials
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours  80%
Semester Assessment Aberystwyth Assessment. Coursework - Examples Class. Deadline: Week 4 of the Semester10%
Semester Assessment Cardiff Assessment. Course Work - Examples Class. Deadline: Week 10 of the Semester10%
Supplementary Exam2 Hours Supplementary exam  100%

Learning outcomes

After taking this module students should be able to:

INFORMATION THEORY

• Justify the use of log(p) as a definition of information
• Calculate the entropy/uncertainty associated with a probability distribution
• Apply the concept of entropy in an analysis of communication systems with and without noise
• Analyse the performance of a 1D array of detectors and the information content of a mass spectrum peak in terms of information theory
• Show the relationship between 'Information Theory Entropy' and 'Thermodynamic entropy'.

ASTROPHYSICAL APPLICATIONS
• Derive and apply the hydrostatic equilibrium equation for spherically-symmetric stars.
• Distinguish between normal stars governed by the Maxwell-Boltzmann law and degenerate stars governed by the laws of the Fermi-Dirac statistics.
• Be capable of formulating the condition of degeneracy of the stellar gas in terms of the participating physical parameters.
• Derive the equation of state for degenerate non-relativistic and relativistic electron gases using the Fermi-Dirac distribution function.
• Perform a qualitative derivation of the Chandrasekhar limit for masses of white dwarfs and neutron stars in terms of fundamental constants.
• Use the statistical mechanics of solid bodies for evaluation of heat capacity and cooling times of white dwarfs.
• Name, describe and explain in detail various phenomena in laboratory and cosmic physics which are governed by the universal laws of quantum statictical mechanics.

Brief description

This module will be taught jointly with the Department of Physics at Cardiff, using the University of Wales video network. It consists of two blocks of lectures covering different applications of statistical physics:
(a) Information Theory (Aberystwyth)
(b) Astrophysical applications (Cardiff)

Content

Information Theory:
Information - the relation to probability
The message, the bit, message transmission - source, channel, destination, channel capacity, noise
Entropy and information rate
Mutual information
The binary symmetric channel (BSC)
Application in Communications, Spectroscopy and Statistical Mechanics
Identical, indistinguishable Bose and Fermi particles

Astrophysical Applications:
Equilibrium and stability of stars. Gravitational forces and pressure gradients. Normal and degenerate stars.
Breakdown of Maxwell-Boltzmann gas law. Fermi-Dirac/Bose-Einstein statistics. Equation of state for ideal Fermi gas.
White dwarfs. Simple equations of state. Nonrelativistic and ultrarelativistic electrons.
Masses and radii of white dwarfs. The Chandrasekhar limit. Qualitative derivation of the Chandrasekhar limit.
Statistical mechanics of solids and cooling of white dwarfs. Comparison with observations.
Neutron stars. Masses and radii of neutron stars. Pulsars. Observations.

Transferable skills

Example classes, Tutorials.

Reading Lists

s
** General Text
L.D. Landau and E.M. Lifshitz (1969) Statistical Physics Addison-Wesley,

Books
A.B. Carlson Communication Systems McGraw-Hill 0071005609
Applebaum Probability and Information C.U.P. 0521555280
F. Mandl Statistical Physics Wiley
Shapiro and Teukolsky Black Holes, White Dwarfs and Neutron Stars Wiley 0471873160

Notes

This module is at CQFW Level 7