PH 614: Statistical Mechanics
Spring 2022 (D. Belitz)
Chapter 1: Principles of Statistical Mechanics (with emphasis on QM)
$1: Statistical description of large systems
1.1 Phase flow of Hamiltonian systems
1.2 Poincare's theorem
1.3 Necessity of a statistical description of many-body systems
$2: Review of statistical ensembles and thermodynamic potential
2.1 Statistical description of macroscopic systems
2.2 The equilibrium state
2.3 Interacting systems
2.4 Reversible and irreversible processes
2.5 Energy, temperature, and entropy
2.6 The laws of thermodynamics
2.7 Thermodynamic potentials
$3: Statistical ensembles
3.1 The concept of statistical ensembles
3.2 The microcanonical ensemble
3.3 The canonical ensemble
3.4 The grand canonical ensemble
3.5 The thermodynamic limit, and the Duhem-Gibbs relation
3.6 Systems in magnetic fields
$4: Quantum statistical mechanics
4.1 The postulates of qantum statistical mechanics
4.2 The statistical operator for various ensembles
4.3 Fermions and bosons
4.4 The Fermi-Dirac distribution
4.5 The Bose-Einstein distribution
Chapter 2: Selected Applications
$1: Classical systems
1.1 The classical monatomic ideal gas
1.2 The Gibbs paradox
1.3 The equipartition theorem
1.4 Maxwell's velocity distribution I: Canonical ensemble
1.5 Maxwell's velocity distribution II: Microcanonical ensemble
$2: The ideal Fermi gas
2.1 Distribution functions, and the equation of state (for both fermions and bosons)
2.2 The degenerate electron gas
2.3 The specific heat of a degenerate electron gas (Sommerfeld expansion)
2.4 Pauli paramagnetism
2.5 Landau diamagnetism
$3: The ideal Bose gas
3.1 Bose-Einstein condensation
3.2 Chemical potential and particle number for T0
3.3 The specific heat of an ideal Bose gas
$4: Blackbody radiation
4.1 Planck's law
4.2 Discussion of Planck's law
Chapter 3: Kinetic Theory