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Description

This is a two-semester course on statistical mechanics. Basic principles examined in 8.333 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, Statistical Mechanics II (8.334). 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

Statistical Physics I (8.044) and Quantum Physics II (8.05).

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. New York, NY: Wiley, 1987. ISBN: 9780471815181.

Pathria, R. K. Statistical Mechanics. New York, NY: Pergamon Press, 1972. ISBN: 9780080189949.

Pippard, A. B. Elements of Classical Thermodynamics for Advanced Students of Physics. Cambridge, UK: University Press, 1966.

Ma, Shang-keng. Statistical Mechanics. Translated by M. K. Fung. Philadelphia, PA: World Scientific, 1985. ISBN: 978-9971966065 (Singapore), 9789971966072 (Singapore: pbk).

Landau, L. D., and E. M. Lifshitz. Statistical Physics. Part 1. 3rd ed. New York, NY: Pergamon, 1980. ISBN: 0080230385.

Reif, Frederick, ed. Fundamentals of Statistical and Thermal Physics. New York, NY: McGraw-Hill, 1965.

Feynman, Richard Phillips. Statistical Mechanics. Reading, MA: Addison-Wesley, 1998. ISBN: 9780201360769.

Problem Sets

The homework assignments are an important part of this course, and the final average homework score will count for 50% 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 12 problem sets. They are due by 5:00 pm on the due date. They are to be turned in at lecture or by arrangement with the TA. No problem sets will be accepted after the solutions have been posted. Problem sets handed in after the 5 pm deadline but before the solutions have been posted are subject to a 50% grade penalty.

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 50% contribution from the (required) problem sets. Thus, perfect scores on all the non-optional problems leads to the maximal grade of 50 from the problem sets. The optional problems provide a chance to reach the 50%-score for the problem sets, even when some of the required problems are not correct.

Exams

There is a midterm exam (quiz) and a final exam. Each exam score will count 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:

Your final letter grade will reflect our best attempt to evaluate objectively your performance in the course:

A: Exceptionally good performance, demonstrating a superior understanding of the subject matter, a foundation of extensive knowledge, and a skillful use of concepts and/or materials.

B: Good performance, demonstrating capacity to use the appropriate concepts, a good understanding of the subject matter, and an ability to handle the problems and materials encountered in the subject.

C: Adequate performance, demonstrating an adequate understanding of the subject matter, an ability to handle relatively simple problems, and adequate preparation for moving on to more advanced work in the field.

D: Minimally acceptable performance, demonstrating at least partial familiarity with the subject matter and some capacity to deal with relatively simple problems, but also demonstrating deficiencies serious enough to make it inadvisable to proceed further in the field without additional work.

F: Failed. This grade also signifies that the student must repeat the subject to receive credit.