Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Course Description

In this course we will discuss principles and methods of statistical mechanics. Topics will include: classical and quantum statistics, grand ensembles, fluctuations, molecular distribution functions, and other topics in equilibrium statistical mechanics. Topics in thermodynamics and statistical mechanics of irreversible processes will also be covered.

Prerequisites

5.70 Statistical Thermodynamics with Applications to Biological Systems
5.73 Introductory Quantum Mechanics I
18.075 Advanced Calculus for Engineers

Textbooks

The following is a list of recommended textbooks that you may find useful for this course. No required readings will be assigned.

Buy at Amazon Groot, Sybren Ruurds de, and Peter Mazur. Non-Equilibrium Thermodynamics. Dover Publications, 2011. ISBN: 9780486647418.

Buy at Amazon Van Kampen, N. G. Stochastic Processes in Physics and Chemistry. Elsevier, 2007. ISBN: 9780444529657. [Preview with Google Books]

Buy at Amazon Boon, Jean-Pierre, and Sidney Yip. Molecular Hydrodynamics. McGraw-Hill, 1980. ISBN: 9780070065604.

Buy at Amazon Reichl, Linda E. A Modern Course in Statistical Physics. Wiley-Interscience, 1998. ISBN: 9780471595205.

Buy at Amazon Hansen, Jean-Pierre, and Ian R. McDonald. Theory of Simple Liquids. Elsevier Academic Press, 2006. ISBN: 9780123705358. [Preview with Google Books]

Buy at Amazon McQuarrie, Donald A. Statistical Mechanics. University Science Books, 2000. ISBN: 9781891389153. [Preview with Google Books]

Assignments

There will be 6 problem sets assigned. They will be graded.

Final Project

You will have to complete a final project at the end of the term. You will be given a set of problems to work on outside of class.

Grading

This course will be graded based on the following:

ACTIVITIES PERCENTAGES
Class participation 10%
Four problem sets 50%
Final project 40%

Calendar

Please note: each chapter of lecture notes is multiple lectures, and each section is roughly equivalent to one week.

CHAPTER # TOPICS SUBTOPICS
1 Stochastic Processes and Brownian Motion

1.1 Markov Processes

1.1.1 Probability Distributions and Transitions

1.1.2 The Transition Probability Matrix

1.1.3 Detailed Balance

1.2 Master Equations

1.2.1 Motivation and Derivation

1.2.2 Mean First Passage Time

1.3 Fokker-Planck Equations

1.3.1 Motivation and Derivation

1.3.2 Properties of Fokker-Planck Equations

1.4 The Langevin Equation

1.5 Appendix: Applications of Brownian Motion
2 Non-equilibrium Thermodynamics

2.1 Response, Relaxation, and Correlation

2.2 Onsager Regression Theory

2.3 Response Response Theory and Causality

2.3.1 Response Functions

2.3.2 Absorption Power Spectra

2.3.3 Causality and the Kramers-Kronig Relations
3 Hydrodynamics and Light Scattering

3.1 Light Scattering

3.2 Navier-Stokes Hydrodynamic Equations

3.3 Transport Coefficients
4 Time Correlation Functions

4.1 Short-time Behavior

4.2 Projection Operator Method

4.3 Viscoelastic Model

4.4 Long-time Tails and Mode-coupling Theory