Stony Brook University, Department of Physics and Astronomy

 

STATISTICAL MECHANICS
(PHY 540)

Spring 2010

 

A. Logistics

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 E. Lifshitz, Statistical Physics, Pt. 1, 3rd ed. (Pergamon 1980 or a later re-printing)

 

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%

 

B. Syllabus

 

            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.

 

 

C. Course materials

(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.

Selected Physical Constants

 

D. University-mandated statements

Americans with Disabilities Act: If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room128, (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

 Academic Integrity: Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report and suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/ .

 Critical Incident Management: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.