Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1.5 hours / session

Description

This is a two-semester course on statistical mechanics. Basic principles examined in this course are: The laws of thermodynamics and the concepts of temperature, work, heat, and entropy, postulates of classical statistical mechanics, microcanonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas, quantum statistical mechanics; Fermi and Bose systems, interacting systems: Cluster expansions, van der Waal's gas, and mean-field theory.

Topics from modern statistical mechanics are explored in the next course in this sequence, 8.334 Statistical Mechanics II. These include: The hydrodynamic limit and classical field theories; phase transitions and broken symmetries: Universality, correlation functions, and scaling theory; the renormalization approach to collective phenomena; dynamic critical behavior; random systems.

Prerequisites

8.044 Elementary Statistical Mechanics and 8.07 Quantum Mechanics.

Outline Overview

1. Thermodynamics: Thermal equilibrium, the laws of thermodynamics; temperature, energy, entropy, and other functions of state. (4 Lectures)
2. Probability Theory: Probability densities, cumulants and correlations; central limit theorem; laws of large numbers. (2.5 Lectures)
3. Kinetic Theory: Phase space densities; Liouville's theorem, BBGKY hierarchy, the Boltzmann equation; transport phenomena. (4.5 Lectures)
4. Classical Statistical Mechanics: Postulates; microcanonical, canonical and grand canonical ensembles; non-interacting examples. (3 Lectures)
5. Interacting Systems: Virial and cluster expansions; van der Waals theory; liquid-vapor condensation. (4 Lectures)
6. Quantum Statistical Mechanics: Quantization effects in molecular gases; phonons, photons; density matrix formulation. (3 Lectures)
7. Identical Particles: Degenerate quantum gases; Fermi liquids; Bose condensation; superfluidity. (5 Lectures)

Textbooks

This course does not follow a particular text. The following are useful reference books:

Huang, Kerson. Statistical Mechanics. 2nd ed. Wiley, 1987. ISBN: 9780471815181.

Pathria, R. K. Statistical Mechanics. Pergamon Press, 1972. ISBN: 9780080189949. [Preview with Google Books]

Pippard, A. B. The Elements of Classical Thermodynamics for Advanced Students of Physics. University Press, 1966. [Preview with Google Books]

Ma, Shang-keng. Statistical Mechanics. Translated by M. K. Fung. World Scientific Publishing Company, 1985. ISBN: 9789971966065.

Landau, L. D., and E. M. Lifshitz. Statistical Physics, Part 1. 3rd ed. Pergamon Press, 1980. ISBN: 9780080230382.

Reif, Frederick, ed. Fundamentals of Statistical and Thermal Physics. McGraw-Hill, 1965. [Preview with Google Books]

Feynman, Richard Phillips. Statistical Mechanics: A Set of Lectures. Westview Press, 1998. ISBN: 9780201360769. [Preview with Google Books]

Kardar, Mehran. Statistical Physics of Particles. Cambridge University Press, 2007. ISBN 9780521873420. [Preview with Google Books]

Problem Sets

The homework assignments are an important part of this course, and the final average homework score will count for 30% of the final grade. You may consult with classmates in "study groups," as long as you write out your own answers, and do not use solution-sets from previous years.

There are 6 problem sets. Occasionally, there are problems marked as optional in the problem sets. If attempted, these problems will be graded as other problems, and their score added to the total. The overall grade for the course has a 30% contribution from the (required) problem sets. Thus, perfect scores on all the non-optional problems leads to the maximal grade of 30 from the problem sets. The optional problems provide a chance to reach the 30%-score for the problem sets, even when some of the required problems are not correct.

Exams

There are 3 in-class tests and a final exam. The in-class tests each count for 15% of the final grade. The Final Exam counts for 25% of the final grade.

A missed midterm will be averaged into the final grade as zero, unless an excuse is obtained in advance. Excuses are granted only for very serious circumstances attested to by the Dean or a medical doctor. A student who has been excused may be required to take a makeup exam.

Grading

Final grades will be determined from: