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 graduatelevel 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:
 Format: Lecture and discussion
 Course Material: Reading & Lecture Notes
 Evaluation: Exercises and Exams
 PreRequisites: undergraduate classical and quantum mechanics and statistical physics
Topics:
Syllabus
 Stochastic Processes in Physics
 Brownian Motion
 Random Walks and Diffusion
 Langevin's Theory of Brownian Motion
 Classical Statistical Physics I
 Maxwell's Velocity Distribution
 Equipartition Theorem
 Ideal Gas Equation of State
 Classical Statistical Physics II
 Hydrodynamics & Diffusion
 FokkerPlanck Equation
 Boltzmann's Kinetic Theory of Gases
 Statistical Ensembles  Gibbs Formulation
 Hamiltonian Dynamics & Phase Space
 Distribution Functions
 Mean values
 Entropy in Statistical Mechanics
 Gibbs Free Energy
 Timeevolution & Liouville's Theorem
 Entropy and Approach to Equilibrium
 Canonical and Grand Ensembles
 Partition Functions
 Statistical Theory of Thermodynamics
 Maxwell's Velocity Distribution derived
 Grand Canonical Ensemble
 Thermodynamic Potential
 Interacting Gases & Liquids
 Cluster expansions
 Virial expansion & virial coefficient
 Equation of state for imperfect gases
 Correlations and scattering theory

 Quantum Statistical Mechanics I
 Hilbert Space vs. Phase Space
 Partition Function  Quantum Theory
 Ideal Fermi Gas  Thermodynamics
 ZeroPoint Pressure of a Fermi Gas
* Sommerfeld's Theory of Free Electrons
* Pauli's Theory of Paramagnetism
* White Dwarfs and Neutron Stars
 Quantum Statistical Mechanics II
 Ideal Bose Gas  Thermodynamics
 Ideal Bose Gas Equation of State
 BoseEinstein Condensation (BEC)
* BEC in Trapped Atomic Gases
* Radiation & Planck's Distribution
* Einstein & Debye Theory of Solids
 Phase Transitions
 Heisenberg Model and Ferromagnetism
 MeanField Theory of Ferromagnetism
 Symmetry Breaking Phase Transitions
 Landau Theory of 2^{nd} Order Transitions
 Fluctuations & Symmetry Breaking
* Spin Waves in Ferromagnets
* Ferroelectric Transitions
* Interacting BECs  Superfluidity
 Weak disturbances from Equilibrium
 Kubo's Theory: Causality, Analyticity
 FluctuationDissipation Theorem
 Noise and Stochastic Processes
 Nyquist Theorem
* Applications

References
 Statistical Mechanics, K. Pathria and P. Beale, 4th edition. Link to online version [
local link].
File translated from
T_{E}X
by
T_{T}H,
version 4.16.
On 18 Jan 2023, 16:14.