Statistical Mechanics (PHY 540) Fall 2021

Lectures: Humanities #3018, TUTH 8:00-9:20AM

Office hours: Tuesdays 10am-12pm

Course Syllabus: (PDF)

Instructor

Sergey Syritsyn (office C-140)
sergey.syritsyn[at]stonybrook.edu

Lectures

28 lectures starting August 24, TUTH 8:00-9:20AM, Humanities #3018

Lecture Notes

Will be posted online (both Blackboard and this page)

Office Hours:

Tuesdays 10am-12pm

TA and Grading

Gonenc Mogol gonenc.mogol[at]stonybrook.edu

Main textbooks

[1] L.Landau and E.Lifshitz, "Statistical Physics, Pt.1", 3rd ed.
[2] K. Huang, "Statistical Mechanics", 2nd ed.
[3] K.Likharev, "Essential Graduate Physics, Part SM", posted online.

Homeworks

Weekly, due in class, deadlines 1 week after handout
Full grade will be given only for unassisted work
Grades and solutions next Tuesday

Course grading

Homeworks: 25%
Midterm exam: 25%
Final exam: 50%

Exams

Open books

Midterm exam: Oct 21 (Thu) regular class time
Final: Dec 8 (Wed) 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.

Announcements

Lecture Notes

  1. Thermodynamics 1 (pages 1-6)
  2. Thermodynamics 2 (pages 7-14)
  3. Principles of Statistics 1 (pages 1-10)
  4. Principles of Statistics 2 (pages 11-22)
  5. Classical, Fermi, Bose gases 1 (pages 1-9)
  6. Classical, Fermi, Bose gases 2 (pages 10-16)
  7. Phase transitions 1 (pages 1-12)
  8. Phase transitions 2 (pages 13-20)
  9. Fluctuations (pages 1-11)

Homework

  1. Homework 1(due Thursday Sep 9); [Hints] -- Solutions
  2. Homework 2(due Thursday Sep 16) [Hints] -- Solutions
  3. Homework 3(due Thursday Sep 28) [Hints] -- Solutions
  4. Homework 4(due Tuesday Oct 5) [Hints] -- Solutions
  5. Homework 5(due Tuesday Oct 19) [Hints] -- Solutions
  6. Homework 6(due Tuesday Nov 2) [Hints] -- Solutions
  7. Homework 7(due Tuesday Nov 9) [Hints] -- Solutions
  8. Homework 8(due Tuesday Nov 16) [Hints] -- Solutions
  9. Homework 9(due Tuesday Nov 30)
  10. Homework 10(due Thursday Dec 7, optional)

Exams

  1. Midterm exam (Oct 22) --Solutions