Reduced density matrices of oscillator systems
  We study the evolution of an oscillator interacting via the most general bilinear coupling (with time-independent coefficients) with an ``environment'' consisting of a set of other harmonic oscillators. We are mainly interested in a possibility of using the Fokker-Planck equation to describe this evolution. Studying different interaction Hamiltonians, we show that unambiguous reduction to the Fokker-Planck equation is possible only within the framework of the so called rotating-wave approximation. As special cases we consider in detail the evolution of two coupled oscillators and relaxation of a charged oscillator in a uniform magnetic field. 
V.V.Dodonov, O.V.Man'ko, V.I.Man'ko