Physics 6311: Statistical Mechanics (Thomas Vojta)

Part I: Principles of equilibrium statistical mechanics

0.

Introduction

0.1

Physical description of large systems

0.2

What is statistical physics?

0.3

Why is it important?

0.4

Historical remarks

0.5

Plan of the course

1.

Minireview of thermodynamics (Chandler chapters 1 and 2, Kardar chapter 1)

1.1

Thermodynamic equilibrium

1.2

State variables

1.3

The laws of thermodynamics

1.4

Thermodynamic potentials

1.5

Stability of the equilibrium state

2.

Elementary probability theory (Kardar chapter 2, Reichl chapter 4)

2.1

Definition of probability

2.2

Random variables

2.3

Averages, moments, cumulants and correlation functions

2.4

Examples of distributions

2.5

Central limit theorem

3.

Principles of Statistical Mechanics (Chandler chapter 3, Kardar chapter 4)

3.1

The Statistical Method and Ensembles

3.2

Microcanonical Ensemble

3.3

Canonical Ensemble

3.4

Generalized Ensembles

Part II: Selected applications

4.

Non-interacting systems (Chandler chapter 4, Kardar chapters 4 and 7)

4.1

Photon gas

4.2

Ideal gases of real particles

4.3

Electrons in metals

4.4

Bose-Einstein condensation

5.

Phase transitions (Chandler chapter 5, Pathria chapters 11 and 12)

5.1

Ising model

5.2

Mean-field theory

5.3

Renormalization group