Quantum Degenerate Gases

In this chapter, we discuss the main results of quantum statistical mechanics required for an understanding of the behavior of ultracold atomic gases, also assuming that the reader is already familiar with general principles of thermodynamics and statistical mechanics as from standard textbooks on these subjects. We first review basic concepts of equilibrium statistical mechanics with particular emphasis on the statistical ensembles and then proceed to study Bose and Fermi systems in terms of static and idealized properties, in the presence of spatial confinement. Finally, we discuss the dynamics of bosons in a single occupied state and in the presence of interatomic interactions using effective many-body time-dependent equations.