Statistical Mechanics
Information for students taking the thirdyear 10credit course Statistical Mechanics (the first half of the 20credit module Statistical Mechanics and Solid State II) is now provided through the Yorkshare VLE.
Indicative syllabus:

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; twolevel 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, MaxwellBoltzmann 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, BoseEinstein condensation, with applications to freeelectron metals and nuclear physics (fermions), and liquid ^{4}He and superconductivity (bosons)

Black body radiation: Energy density, pressure

The classical limit: Phase space, classical equipartition theorem
Rex Godby