Stony Brook University, Department of Physics and Astronomy

STATISTICAL MECHANICS
(PHY 540)

Spring 2007

A. Logistics

Instructor: Konstantin Likharev

Office: B-135

Phone: 2-8159

E-mail: klikharev@notes.cc.sunysb.edu

Office hours: Thursdays 3:00 to 4:30 pm

Grader: Nikita Simonian

Office: B-124

Phone: 2-9786

E-mail: nsimonia@ic.sunysb.edu

Office hours: Tuesdays 10:20-11:20 am

Web site: http://rsfq1.physics.sunysb.edu/~likharev/540/S07/

Basic textbook: L. Landau and E. Lifshitz, Statistical Physics, Pt. 1, 3^rd ed. (Pergamon 1980/86)

Also recommended: K. Huang, Statistical Mechanics, 2^nd ed. (Wiley, 1987)

Lectures: Approximately 26 lectures, 1 hour 20 minutes each

Time: Tue-Thu 11:20-12:40 am

Room: B-131

Homeworks: Weekly (with just one or two exceptions)

Exams: Two midterms (February 22^*) and March 29) and a final (May 10)
All exams: books open

Grade components: Homeworks: 30%

Midterms: 30%

Final exam: 40%

*) Notice the date change!

B. Syllabus and Lecture Notes

0. Introduction

Basic notions of statistical physics. Thermodynamics, statistics, and fluctuation theory. Structure of the course.

1. Brief Review of Thermodynamics Lecture Notes

Energy, entropy, temperature, pressure, work and heat. Thermodynamic potentials, the circular diagram. Systems with variable number of particles, chemical potential.

2. Principles of Physical Statistics Lecture Notes (still incomplete)

Statistical ensembles. Probability, probability density, and density matrix. Ergodicity. The basic statistical hypothesis. Microcanonical ensemble and distribution. Definition of entropy, the Boltzmann-Shannon information, irreversible and reversible computing. Canonical ensemble, the Gibbs distribution. Grand canonical ensemble and distribution. The Bose and Fermi distributions. Statistics of quantum oscillators. Blackbody radiation. Phonons in solids, specific heat of a crystal lattice. The Kolmogorov entropy at chaotic motion, its relation to the Lyapunov exponents.

3. Ideal and Not-So-Ideal Gases Lecture Notes (incomplete)

Ideal classical gas: the Boltzmann distribution, thermodynamics. Quantum ideal gases: thermodynamics of the ideal Bose and Fermi gases. The Bose-Einstein condensation. Weak solutions, osmotic pressure. Gases with weakly interacting particles, virial coefficients, van der Waals equation.

4. Phase Transitions

First order phase transitions, phase equilibrium, the Gibbs rule, latent heat, the Clausius-Clapeyron formula, the critical point. Second order phase transitions, The order parameter, critical exponents, their relations. The Landau mean-field theory, the Ginzburg criterion. The Ising model, 1D solution via the transfer matrix, Onsager's solution for 2D case. Numerical (Monte-Carlo) methods, the Metropolis algorithm. The renormalization-group approach.

5. Fluctuations and Dissipation Lecture Notes (just the beginning)

Small fluctuations, average, variance, r.m.s. value. Fluctuations of energy and temperature. Fluctuations of the number of particles, the binomial, Poisson, and Gaussian probability distributions. Fluctuations of pressure. Time dependence of fluctuations, their correlation function and spectral density. The Langevin-Heisenberg-Lax picture of fluctuations. The fluctuation-dissipation theorem. Quantum noise vs. the uncertainty relation in a harmonic oscillator. Shot noise, fluctuations in two-level systems, 1/f noise. Smoluchowski equation, Fokker-Planck equation, Kramers formula.

6. Elements of Kinetics

The Liouville theorem, the Boltzmann equation; the relaxation-time approximation. Conduction of degenerate Fermi gas, relation to the Drude formula, the drift-diffusion equation.