PHY 4523 - Spring 2001
Topics To Be Covered in the Lectures

Statistical Mechanics in the Microcanonical Ensemble

Thermodynamic processes in closed systems: removal of internal constraints, reversible vs irreversible processes. Thermal equilibrium: statistical equivalents of temperature and entropy. General equilibrium: statistical equivalents of pressure and chemical potential. Einstein model of lattice vibrations. Two-level model of atomic systems. 1D polymer model.   Further reading: Reif Sections 3.1-3.3 and 3.7-3.10; Callen Sections 15.2-4.

Statistical Mechanics in the Canonical and Grand Canonical Ensembles

System in thermal contact with a heat reservoir: canonical probability function. Calculation of macroscopic observables: statistical equivalent of the Helmholtz free energy. Factorizable systems and canonical treatment of microscopic systems. Einstein model and two-level model (revisited). Zipper model of DNA. Variable particle number: the grand canonical probability function. Entropy as a measure of disorder.   Further reading: Reif Sections 6.1, 6.2, 6.3 through Eq. (6.3.8), 6.5, 6.6, 6.9, 6.10.

Classical Systems of Noninteracting Particles

Canonical formulation for classical systems. Monatomic ideal gas: Gibbs' paradox. Equipartition.   Further reading: Reif Sections 7.1-7.6.

Quantum Mechanical Systems of Distinguishable, Noninteracting Particles

Lattice specific heats: Einstein model (covered previously). Paramagnetism.   Further reading: Reif Sections 7.8,7.8.

Quantum Mechanical Systems of Indistinguishable, Noninteracting Particles

Bosons and fermions. Photon statistics. Bose-Einstein statistics. Fermi-Dirac statistics. Maxwell-Boltzmann statistics. The classical limit.   Further reading: Reif Sections 9.1-9.8

Quantum Mechanical Ideal Gases

Density of states of a 3D ideal gas. The classical limit. Rotation/vibration in polyatomic gases. Electromagnetic radiation in a closed cavity. Electromagnetic radiation emitted by a body. The ideal Fermi fluid.   Further reading: Reif Sections 9.9-9.16

Interacting Particles

Vibrational modes of 1D monatomic and diatomic chains. Lattice vibrations: Einstein and Debye models. Ferromagnetism: nearest-neighbor Ising model.   Further reading: Reif Sections 10.1, 10.2, and 10.6

Kinetic Theory of Dilute Gases

Maxwell velocity distribution. Equilibrium rate of molecules striking a surface. Equilibrium pressure exerted by a gas. Gases out of equilibrium: relaxation time and mean free path. Self-diffusion of a mixture of gases.   Further reading: Reif Sections 7.9-7.11, 12.1, 12.2, and 12.5