My third-year 10-credit course Statistical Mechanics, last given in 2019/20, was the first half of the 20-credit module Statistical Mechanics and Solid State II. Indicative syllabus of my course:
- Microstates: microstates (quantum states) and macrostates of a system, degeneracy W, density of states, illustration for a set of N harmonic oscillators, principle of equal equilibrium, probability of an isolated system, term “microcanonical ensemble”
- Thermal equilibrium, temperature: statistical nature of equilibrium illustrated for 2 systems of N harmonic oscillators, definition of temperature, Boltzmann distribution, partition function Z, term “canonical ensemble”
- Entropy: general statistical definition of entropy S, law of increase of entropy, entropy of isolated system in internal equilibrium (“microcanonical ensemble”), entropy of system in thermal equilibrium with a heat bath (“canonical ensemble”), Helmholtz free energy F; equivalence of classical and statistical entropy
- Elementary applications: Vacancies in solids; two-level systems (including magnetic susceptibility of dilute paramagnetic salt), simple harmonic oscillator (partition function, heat capacity).
- Vibrational heat capacity of solids: Quantisation of phonon modes, labelling of modes using wavevector; Einstein and Debye models
- Ideal gas: Partition function of monatomic gas, classical gas law, Maxwell-Boltzmann speed distribution, molecular gases (rotation and vibration), classical limit of occupation numbers
- Systems with variable number of particles: Grand canonical ensemble, chemical potential, Gibbs distribution
- Identical particles: Fermions and bosons, Fermi and Bose distributions, Bose-Einstein condensation, with applications to free-electron metals and nuclear physics (fermions), and liquid 4He and superconductivity (bosons)
- Black body radiation: Energy density, pressure
- The classical limit: Phase space, classical equipartition theorem
From 2020/21, Statistical Mechanics is taught by Dr Paul Davies.