|Module Title||STATISTICAL PHYSICS|
|Co-ordinator||Dr Keith Birkinshaw|
|Other staff||Dr L Grischuck (Cardiff), Dr S Hands (Swansea)|
|Pre-Requisite||Successful Completion of Year 3 of the MPhys Scheme|
|Course delivery||Lecture||20 lectures|
|Seminars / Tutorials||3 seminars / tutorials|
|Assessment||Course work||Examples Class Deadline: Week 4 of the Semester||7%|
|Course work||Examples Class Deadline: Week 8 of the Semester||7%|
|Course work||Examples Class Deadline: Week 11 of the Semester||7%|
Students should be able to derive and apply the hydrostatic equilibrium equation for spherically-symmetric stars. They should be able to distinguish between normal stars governed by the Maxwell-Boltzmann law and degenerate stars governed by the laws of the Fermi-Dirac statistics, and be capable of formulating the condition of degeneracy of the stellar gas in terms of the participating physical parameters. Using the Fermi-Dirac distribution function, you will be able to derive the equation of state for degenerate non-relativistic 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. liquid-vapour, ferromagnetic
Classical thermodynamics conditions for phase equilibrium
The Clausius-Clapeyron 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 - the relation to probability
The message, the bit, message transmission - source, channel, destination, channel capacity, noise
Entropy and information rate
The binary symmetric channel (BSC)
Application in Communications, Spectroscopy and Statistical Mechanics
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.