Coherent states in the problem of the establishment of statistical equilibrium in a system coupled to a thermal bath

A system consisting of a thermal bath and a small system interacting with it is considered. The thermal bath is regarded as a system with very many (in practice infinitely many) degrees of freedom. The small system is coupled to the thermal bath by a fairly weak interaction, which is switched on at the initial time. It is assumed that initially the thermal bath was in a chaotic state, while the small system was in a certain arbitrary state. The method of coherent states is used to show that statistical equilibrium is established in the system coupled to the thermal bath. The evolution of the coherent states are studied by the method of time-dependent invariants.