PHYS 8310

ADVANCED STATISTICAL PHYSICS

 

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, New York, 1985

Supplementary text: H.S.Robertson, Statistical Thermophysics, Prentice, Englewood Cliffs, NJ, 1993.
SYLLABUS

1. Thermodynamics

  1. Macroscopic and microscopic description.
  2. Internal energy, work and heat. Perfect and imperfect differentials
  3. Carnot theorem. Entropy and the Second Law. Maximum of entropy and equilibrium.
  4. Fundamental relations. Entropy of ideal gas. Van der Waals fluid.
  5. Entropy of mixture. Chemical potential.
  6. Maximum work theorem. Thermodynamic potentials.
  7. Equilibria and minima of potentials.
  8. Thermodynamic identities. Maxwell identities and Gibbs-Duhem relations. Reduction of derivatives, method of Jacobians.
  9. Stability and thermodynamic inequalities.
  10. Phases and Gibbs phase rule.
  11. Thermodynamic fluctuations.

2. Equilibrium statistical mechanics

  1. Principle of maximum disorder and Gibbs distribution.
  2. Microcanonical, canonical, and grand canonical ensembles.
  3. Monatomic ideal gas.
  4. Einstein and Debye heat capacity.
  5. Rotational contribution to heat capacity.

3. Ideal quantum gases

  1. Fermi gas. Grand partition function. Fermi distribution and Fermi energy. Heat capacity.
  2. Application to astrophysics. Equilibria of stars.*
  3. Bose systems. Bose condensation.
  4. Black body radiation. Photons and Planck distribution.
  5. Thermodynamic fluctuations in ideal gases.

4. Dielectric and magnetic systems

  1. Polarization and electrostatic energy.*
  2. Dielectrics with fixed external potentials. Free energy of dielectrics.*
  3. Microscopic models of dielectrics. Rigid and induced dipoles.*
  4. Thomas-Fermi approximation for interacting electron gas. Debye screening. Plasmons.
  5. Thermodynamics of magnetics.
  6. Pauli paramegnetism and Landau diamagnetism. Quantum oscillations.

5. Thermodynamic of phase transitions

  1. Phase transitions and stability.
  2. Classification of phase transition. Transitions of first and second order.
  3. First order transitions. Latent heats. Clapeyron relation.
  4. Second order transitions. Landau theory.
  5. Critical exponents. Scaling.*
  6. Critical fluctuations and Ginzburg criterion.*

6. Phase transitions in systems of interacting particles*

  1. Ising model in one dimension
  2. Ising model in 2d.
  3. Kadanoff renormalization.
  4. Wilson renormalization.

7. Irreversible processes*

  1. Kinetic coefficients.
  2. Onsager relations
  3. Boltzmann equation. Relaxation-time approximation.
  4. Liouville equation. Quantum Liouville equation.
  5. Linear response theory. Kubo formulas.
  6. Fluctuation-Dissipation theorem

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