Dynamics of a subsystem interacting with a thermal bath

A simple and rigorous derivation of an exact quantum kinetic equation for the density matrix of a subsystem in contact with a thermal bath is proposed. The Markov approximation of this equation is studied. A quantum evolution equation is also obtained for the equilibrium two-time correlation functions of the dynamical variables of the subsystem. As an application, a particle (oscillator) interacting with an arbitrary medium in thermodynamic equilibrium through any power of the particle displacement operator is considered.