# Statistical Mechanics (PHY 540) Fall 2017

### Lectures: Harriman Hall #112, TUTH 8-9:20AM

### Office hours: Physics C-140, Tuesdays 10am-12pm

###

Course Syllabus: (PDF) or (DOC)

### Instructor

Sergey Syritsyn (office C-140)

sergey.syritsyn[at]stonybrook.edu
### Lectures

28 lectures starting Aug 29, TUTH 8-9:20AM, Harriman Hall #112
### Lecture Notes

Will be posted online
### Office Hours:

Tuesdays 10am-12pm, Physics C-140
### TA and Grading

Gongjun Choi (gongjun.choi[at]stonybrook.edu)
### Main textbooks

[1] L.Landau and E.Lifshitz, "Statistical Physics, Pt.1", 3^{rd} ed.

[2] K. Huang, "Statistical Mechanics", 2^{nd} ed.

[3] K.Likharev, "Essential Graduate Physics, Part SM",
posted online.
### Homeworks

Weekly, deadline 1 week after handout

Grades and solutions 1 week after the deadline
### Course grading

Homeworks: 25%

Midterm: 25%

Final exam: 50%
### Exams

Open books
Midterm: Oct 5

Final Dec 12, 11:15am-1:45pm

### 1. Introduction and Review of Thermodynamics

Basic notions of statistical physics and thermodynamics: energy, entropy,
temperature, work and heat. Thermodynamic potentials and circular diagram. Heat
capacity and equation of state. Thermodynamics of ideal gas. Systems with
variable number of particles and chemical potential.
### 2.Principles of Physical Statistics

Statistical ensembles and ergodicity. Probability, probability density, and
density matrix. Microcanonical ensemble and the basic statistical hypothesis.
Definition of entropy and relation to information. Canonical ensemble and the
Gibbs distribution. Statistics of quantum oscillator, photons and blackbody
radiation, phonons and heat capacity of crystals lattices. Grand canonical
ensemble and distribution. The Boltzmann, Bose and Fermi distributions in
systems of independent particles.
### 3. Ideal and Weakly Interacting Gases.

Thermodynamics of ideal classical gas and the Maxwell distribution. The Gibbs
paradox. Quantum ideal gases, the Fermi sea and the Bose-Einstein condensation.
Gases with weakly interacting particles.
### 4.Phase Transitions

First order phase transitions, phase equilibrium, latent heat, critical point,
the Gibbs rule. The van der Waals equation. The Clausius-Clapeyron formula.
Weak solutions, osmotic pressure. Second order phase transitions, the order
parameter, critical exponents. Landau's mean field theory and the Ginsburg
criterion. The Ising model, 1D solution via transfer matrix, Onsager's solution
for 2D case. Numerical Monte Carlo methods, the Metropolis and the “heatbath”
update algorithms. Renormalization group.
### 5. Fluctuations and Dissipations

Small fluctuations, variance, r.m.s. fluctuation. Fluctuations of energy and
the number of particles. Fluctuations of temperature and volume. Time
dependence of fluctuations, their correlation and spectral density. The
fluctuation-dissipation theorem. Quantum noise and the uncertainty relation.
The Einstein-Smoluchowski equation, the Fokker-Planck equation.
### 6. Elements of Kinetics

The Liouville theorem; the Boltzmann equation; the relaxation time
approximation. Conduction of degenerate Fermi gas, electrochemical potential,
thermoelectric effects, the Onsager reciprocal relations.