Department of Physics and Astronomy
PHYS 8310 - ADVANCED STATISTICAL
PHYSICS
Fall Semester 2006
Tuesday, Thursday 1:00-2:15 pm --- 272 Natural Sciences Center
Instructor: Mark Stockman
Office: 455 Science Annex
Phone: (404)651-2779
E-mail: mstockman@gsu.edu
Web site: http://www.phy-astr.gsu.edu/stockman/
Grading: 30% midterm exam, 70% final exam
Final
Exam: Tuesday, December 12 from
Text: L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1 (Paperback - 544 pages, 3 edition), Vol. 5, 1980, Butterworth Heinemann; ISBN: 0750633727
Supplementary text: H. B. Callen, Thermodynamics and Introduction
to Thermostatistics, Wiley,
Basic Rules of the Class Room
These rules are designed to
allow students to get the maximum benefit for their time and money spent.
The physical attendance of lectures is not required but strongly recommended.
If you happen to be late, enter class, do not apologize, quietly take your seat
and start working. If you need to leave, do so also as quietly as possible, do
not ask permission.
Do not talk in class even in a low voice since it is disruptive (asking
a fellow student a brief question is admissible, but should be kept to the
minimum). Do not hesitate to interrupt the lecturer with any questions or
comment, since it is beneficial for the class. (Do not assume that your
question is too trivial to ask -- it may well be not so trivial. Many students
may have a similar problem. No questions and comments in class will affect your
grades in any way.)
At the exams, you may not use any notes or books, unless specifically allowed.
You may briefly (for not more than five minutes) leave the class room after one
hour of work without asking permission. You should bring your calculator (no
data banks) and pen, or pencils. The paper needed will be given to you. The
date and time of the final exam cannot be changed.
SYLLABUS
1. Thermodynamics
Macroscopic and microscopic description.
Internal energy, work and heat. Perfect and imperfect differentials
Carnot theorem. Entropy and the Second Law. Maximum of entropy and equilibrium.
Fundamental relations. Entropy of ideal gas. Van der Waals fluid.
Entropy of mixture. Chemical potential.
Maximum work theorem. Thermodynamic potentials.
Equilibria and minima of potentials.
Thermodynamic identities. Maxwell identities and Gibbs-Duhem relations. Reduction of derivatives, method of Jacobians.
Stability and thermodynamic inequalities.
Phases and Gibbs phase rule.
Thermodynamic fluctuations.
2. Equilibrium statistical mechanics
Principle of maximum disorder and Gibbs distribution.
Microcanonical, canonical, and grand canonical ensembles.
Monatomic ideal gas.
Einstein and Debye heat capacity.
Rotational contribution to heat capacity.
3. Ideal quantum gases
Fermi gas. Grand partition function. Fermi distribution and Fermi energy. Heat capacity.
Application to astrophysics. Equilibria of stars.*
Bose systems. Bose condensation.
Black body radiation. Photons and Planck distribution.
Thermodynamic fluctuations in ideal gases.
4. Dielectric and magnetic systems
Polarization and electrostatic energy.*
Dielectrics with fixed external potentials. Free energy of dielectrics.*
Microscopic models of dielectrics. Rigid and induced dipoles.*
Thomas-Fermi approximation for interacting electron gas. Debye screening. Plasmons.
Thermodynamics of magnetics.
Pauli paramegnetism and Landau diamagnetism. Quantum oscillations.
5. Thermodynamic of phase transitions
Phase transitions and stability.
Classification of phase transition. Transitions of first and second order.
First order transitions. Latent heats. Clapeyron relation.
Second order transitions. Landau theory.
Critical exponents. Scaling.*
Critical fluctuations and Ginzburg criterion.*
6. Phase transitions in systems of interacting particles*
Ising model in one dimension
Ising model in 2d.
Kadanoff renormalization.
7. Irreversible processes*
Kinetic coefficients.
Onsager relations
Boltzmann equation. Relaxation-time approximation.
Liouville equation. Quantum Liouville equation.
Linear response theory. Kubo formulas.
Fluctuation-Dissipation theorem
*) Time permitting