Statistical Physics (U01443)

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

This is a course on the statistical physics of interacting particles. We begin by reviewing the fundamental assumptions of equilibrium statistical mechanics focussing on the relation between missing information (or entropy) and probability. We then consider the statistical mechanics of interacting particles and develop important approximation schemes. This leads us to review phase transitions and the unifying phenomenology. We study in detail a simple, microscopic model for phase transitions: the Ising model. We then consider a general theoretical framework known as
Landau Theory. Finally we discuss the issue of dynamics: how does a system approach and explore the state of thermal equilibrium? How does one reconcile microscopic time reversibility with the macroscopic arrow of time?

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

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 and distinguish between the Boltzmann and Gibbs
entropies

2) Derive the principal ensembles of Statistical Physics
by using the method of Lagrange multipliers to maximise the Gibbs entropy

3) Discuss the many-body problem and be able to formulate and motivate various approximation schemes.

4) Describe the phenomenolgy of phase transitions
in particular Bose-Einstein condensation, liquid-gas transition and ferromagnetic ordering.

5) Formulate the Ising model of phase transitions and be able to motivate and work out various mean-field theories

6) Articulate the paradox of the arrow of time.

7) Formulate mathematical descriptions of dynamics such as Fermi's master equation, Langevin equations and the diffusion equations; solve simple examples of such descriptions such as random walks and Brownian motion

8) Discuss and formulate fluctuation-dissipation relations and linear correlation and response theory