Statistical Physics (U01443)

? Credit Points : 10 ? SCQF Level : 11 ? Acronym : PHY-4-StatPh

This is a course in the statistical physics of interacting particles. We study the basic physics of phase transitions, with the aid of the Ising model of magnetism. This model exhibits spontaneous symmetry breaking. We also discuss the issue of dynamics: how does a system approach and/or explore the state of thermal equilibrium?

Entry Requirements

? Pre-requisites : At least 80 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule Q.

Variants

? This course has variants for part year visiting students, as follows

Statistical Physics (VS1) (Semester 1 (Blocks 1-2))

Subject Areas

Home subject area

Undergraduate (School of Physics), (School of Physics, Schedule Q)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
21/09/2006	09:00	10:00	Lecture Room 3218, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	09:00	09:50	KB
Lecture	Thursday	09:00	09:50	KB

Summary of Intended Learning Outcomes

Upon successful completion of this course it is intended that a student will be able to:
1)Define the term microstate and explain its significance as a solution of the N-body equation of motion
2)Distinguish between equilibrium and nonequilibrium macrostates
3)Appreciate and be able to resolve the paradox inherent in
describing macroscopic irreversible systems in terms of microscopic reversible processes
4)Explain the concept of an `ensemble of systems' and state the constraints involved in the MCE, CE and GCE
5)State the Boltzmann and Gibbs expressions for the entropies and derive the relationship between them
6)Derive the equilibrium probability distribution for an ensemble with two non-trivial constraints and specialize the result to quantum and classical fluids in both CE and GCE, obtaining the `bridge' equations
7)Distinguish between the Hamiltonian for a perfect gas and that for a real gas
8)State the virial theorem and explain the significance of the second virial coefficient
9)Explain what is meant by a bare particle, a dressed particle, a quasi-particle and renormalization; with reference to the concept of a diagonalized Hamiltonian
10)Explain mean-field theory and be able to work out examples for a magnet and a one-component plasma
11)Describe the Ising model and use it to obtain values of critical exponents
12)Derive the Liouville equation and show that a coupled Hamiltonian leads to a coupled set of equations for reduced distribution functions
13)State the Gibbs and Boltzmann H-theorems and explain how
coarse-graining resolves the reversibility paradox
14)Explain the need to close the BBGKY statistical hierarchy in order to derive macroscopic balance equations and discuss how this is achieved by the Boltzmann equation
15)State Fermi's Master equation and use it to derive the Langevin equation and the fluctuation-dissipation relation