Instructor: Konstantin
Likharev
Office:
Room B-135
Phone: 2-8159
E-mail: klikharev@notes.cc.sunysb.edu
Office hours: Thursdays 1:30 to 3:30 pm
Grader:
Nathan Borggren
Office: Room C-121
Phone:
1-520-450-2572
E-mail: nborggren@gmail.com
Office hours:
Thursdays 1:00 to 2:00 pm
Web site: http://mysbfiles.stonybrook.edu/~klikharev/540/S10/
Basic textbook: L. Landau and
Also recommended:
K. Huang, Statistical Mechanics, 2nd ed. (Wiley, 1987)
F.
Schwabl, Statistical Mechanics, 2nd
ed. (Springer, 2009)
Lectures: Approximately 26 lectures, 80 minutes each w/o break
Time:
Tue-Thu 11:20-12:40 am, Room B-131
Homeworks: Weekly, with
just one or two exceptions
Deadline:
one week after assignment handout
Feedback
(including model solutions): one week after deadline
Exams: Midterm: Thursday
March 18, lecture time and room
Final:
Tuesday May 11, 2:15-4:45 pm, lecture room
All
exams: books open
Grade components: Homeworks: 15%
Midterms:
30%
Final
exam: 55%
1.
Introduction and Review of Thermodynamics Lecture notes
Structure of the course.
Basic notions of statistical physics and thermodynamics. Energy, entropy,
temperature, pressure, work and heat. Thermodynamic potentials, the circular
diagram. Thermodynamics of ideal classical gas. Systems with variable number of
particles, chemical potential.
2.
Principles of Physical Statistics Lecture notes
Statistical ensembles;
ergodicity. Probability, probability density, and density matrix.
Microcanonical ensemble; the basic statistical hypothesis. Definition of entropy,
the Boltzmann-Shannon information. The Kolmogorov entropy at deterministic
chaos; its relation to the Lyapunov exponents. Irreversible and reversible
computing. Canonical ensemble, the Gibbs distribution. Statistics of quantum
oscillators. Blackbody radiation. Phonons in solids, specific heat of a crystal
lattice. Grand canonical ensemble and distribution. The Boltzmann, Bose and
Fermi distributions in systems of independent particles.
3. Ideal
and Not-So-Ideal Gases Lecture notes
Ideal classical gas:
the Maxwell distribution, thermodynamics. The Gibbs (gas mixing) paradox.
Quantum ideal gases. The Fermi sea. The Bose-Einstein condensation. Gases with
weakly interacting particles, virial coefficients.
4. Phase
Transitions Lecture notes
First order phase
transitions, the van der Waals equation, phase equilibrium, latent heat, the
Clausius-Clapeyron formula, the critical point, the Gibbs rule. Weak solutions,
osmotic pressure. 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 (time permitting).
5.
Fluctuations and Dissipation Lecture notes
Small fluctuations,
average, variance, r.m.s. value. Fluctuations of energy and the number of particles.
The binomial, Poisson, and Gaussian probability distributions. Fluctuations of
temperature and volume. 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. Shot noise the 1/f noise. The Smoluchowski and
Fokker-Planck equations, the Kramers formula.
6.
Elements of Kinetics Lecture notes
The Liouville theorem,
the Boltzmann equation; the relaxation-time approximation. Conduction of
degenerate Fermi gas, electrochemical potential, thermoelectric effects, the
Onsager reciprocal relations.
(in the
pdf format)
Selected
Mathematical Formulas which may be useful not only for this course, but also for
other graduate Core Physics courses of our department.
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.
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