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
Also recommended: K. Huang, Statistical
Mechanics, 2nd 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!
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.