Equilibration and thermalization in finite quantum systems

Experiments with trapped atomic gases have opened novel possibilities for studying the evolution of nonequilibrium finite quantum systems, which revived the necessity of reconsidering and developing the theory of such processes. This review analyzes the basic approaches to describing the phenomena of equilibration, thermalization, and decoherence in finite quantum systems. Isolated, nonisolated, and quasi-isolated quantum systems are considered. The relations between equilibration, decoherence, and the existence of time arrow are emphasized. The possibility for the occurrence of rare events, preventing complete equilibration, are mentioned.