Module Identifier  PHM1510  
Module Title  STATISTICAL PHYSICS  
Academic Year  2003/2004  
Coordinator  Professor Keith Birkinshaw  
Semester  Semester 1  
Other staff  Dr L Grischuck (Cardiff)  
PreRequisite  Successful Completion of Year 3 of the MPhys Scheme  
Course delivery  Lecture  20 lectures  
Seminars / Tutorials  3 seminars / tutorials  
Assessment 

INFORMATION THEORY
ASTROPHYSICAL APPLICATIONS
Students should be able to derive and apply the hydrostatic equilibrium equation for sphericallysymmetric stars. They should be able to distinguish between normal stars governed by the MaxwellBoltzmann law and degenerate stars governed by the laws of the FermiDirac statistics, and be capable of formulating the condition of degeneracy of the stellar gas in terms of the participating physical parameters. Using the FermiDirac distribution function, you will be able to derive the equation of state for degenerate nonrelativistic and relativistic electron gases. You wil be able to perform a qualitative derivation of the Chandrasekhar limit for masses of white dwarfs and neutron stars in terms of fundamental constants. Students should be able to use the statistical mechanics of solid bodies for evaluation of heat capacity and cooling times of white dwarfs. You will be capable of naming, describing and explaining in details various phenomena in laboratory and cosmic physics which are governed by the universal laws of quantum statistical mechanics.
Phase Transition and Critical Phenomena:
Phenomenology of phase transitions, eg. liquidvapour, ferromagnetic
Classical thermodynamics conditions for phase equilibrium
The ClausiusClapeyron equation
First and Second Order Phase transitions, the order parameter
Statistical mechanics approach: the Ising Model, observables, correlation functions
Mean Field Approximation
Critical Exponents and Universality
Introduction to the Renormalisation Group
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
Astrophysical Applications:
Equilibrium and stability of stars. Gravitational forces and pressure gradients. Normal and degenerate stars.
Breakdown of MaxwellBoltzmann gas law. FermiDirac/BoseEinstein 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.
This module is at CQFW Level 7