Quantum gases

Abstract

AbstractThis chapter presents the statistical description of quantum gases: bosons and fermions. The coarse-grained distribution function, measuring the average occupation of each quantum level is the fundamental object under study. In thermal equilibrium, gases obey the Bose—Einstein and Fermi—Dirac distributions. Out of equilibrium, a semiclassical description is adopted where the distribution functions evolve as particles and move among levels. For bosons, the presence of other particles in the final level enhances the transitions (stimulated emission), while for fermions they suppress the transition (Pauli exclusion principle). These effects are included semiclassically in the kinetic equation. It is shown that the quantum kinetic equation gives the correct evolution toward the equilibrium distributions. Phonons are worked out in detail, where the phonon–phonon and phonon–electron interactions affect the energy transport. Finally, lasers and the quark—gluon plasma are analysed in the context of the theory.