Physics 7225
Statistical Mechanics
Spring 2023
J. A. Sauls

Lectures: Tuesday & Thursday, 9:00 am - 10:20 pm
Where: Room: 105 Nicholson Hall

Statistical mechanics is the set of principles and concepts that provide the foundation for understanding the macroscopic states of matter and radiation in terms of our underlying theory of atomic structure, quantum mechanics - classical mechanics in certain limits - and quantum electrodynamics. Statistical mechanics underpins Thermodynamics, Hydrodynamics and Continuum mechanics, and provides the basis for understanding phase transitions, fluctuations about equilibrium, and the theory of matter and radiation driven out of equilibrium. This is a graduate-level course covering the foundations of statistical mechanics illustrated with applications ranging from the theory of classical and quantum gases, black body radiation, Landau theory of phase transitions, Brownian motion, stochastic dynamics, Langevin theory.

Details:

Topics:

Syllabus

  1. Stochastic Processes in Physics
    1. Brownian Motion
    2. Random Walks and Diffusion
    3. Langevin's Theory of Brownian Motion
  2. Classical Statistical Physics I
    1. Maxwell's Velocity Distribution
    2. Equipartition Theorem
    3. Ideal Gas Equation of State
  3. Classical Statistical Physics II
    1. Hydrodynamics & Diffusion
    2. Fokker-Planck Equation
    3. Boltzmann's Kinetic Theory of Gases
  4. Statistical Ensembles - Gibbs Formulation
    1. Hamiltonian Dynamics & Phase Space
    2. Distribution Functions
    3. Mean values
    4. Entropy in Statistical Mechanics
    5. Gibbs Free Energy
    6. Time-evolution & Liouville's Theorem
    7. Entropy and Approach to Equilibrium
  5. Canonical and Grand Ensembles
    1. Partition Functions
    2. Statistical Theory of Thermodynamics
    3. Maxwell's Velocity Distribution derived
    4. Grand Canonical Ensemble
    5. Thermodynamic Potential
  6. Interacting Gases & Liquids
    1. Cluster expansions
    2. Virial expansion & virial coefficient
    3. Equation of state for imperfect gases
    4. Correlations and scattering theory
  1. Quantum Statistical Mechanics I
    1. Hilbert Space vs. Phase Space
    2. Partition Function - Quantum Theory
    3. Ideal Fermi Gas - Thermodynamics
    4. Zero-Point Pressure of a Fermi Gas
      * Sommerfeld's Theory of Free Electrons
      * Pauli's Theory of Paramagnetism
      * White Dwarfs and Neutron Stars
  2. Quantum Statistical Mechanics II
    1. Ideal Bose Gas - Thermodynamics
    2. Ideal Bose Gas Equation of State
    3. Bose-Einstein Condensation (BEC)
      * BEC in Trapped Atomic Gases
      * Radiation & Planck's Distribution
      * Einstein & Debye Theory of Solids
  3. Phase Transitions
    1. Heisenberg Model and Ferromagnetism
    2. Mean-Field Theory of Ferromagnetism
    3. Symmetry Breaking Phase Transitions
    4. Landau Theory of 2nd Order Transitions
    5. Fluctuations & Symmetry Breaking
      * Spin Waves in Ferromagnets
      * Ferroelectric Transitions
      * Interacting BECs - Superfluidity
  4. Weak disturbances from Equilibrium
    1. Kubo's Theory: Causality, Analyticity
    2. Fluctuation-Dissipation Theorem
    3. Noise and Stochastic Processes
    4. Nyquist Theorem
      * Applications
References
  1. Statistical Mechanics, K. Pathria and P. Beale, 4th edition. Link to online version [ local link].
File translated from TEX by TTH, version 4.16.
On 18 Jan 2023, 16:14.