CLASSICAL AND QUANTUM DISSIPATION IN NONHOMOGENEOUS ENVIRONMENTS

We investigate a generalization of the oscillator model of a particle interacting with a thermal reservoir, in which arbitrary nonlinear cou plings in the particle coordinates are present. The equilibrium positi ons of the heat bath oscillators are promoted to space-time functions, which are shown to represent a modulation of the internal noise by th e external forces. The model thus provides a description of classical and quantum dissipation in non-homogeneous environments. In the classi cal case we derive a generalized Langevin equation with nonlinear mult iplicative noise and a position-dependent fluctuation-dissipation theo rem associated to non-homogeneous dissipative forces. When time-modula tion of the noise is present, a new force term is predicted besides th e dissipative and random ones. The model is quantized to obtain the no n-homogenous influence functional and master equation for the reduced density matrix of the Brownian particle. The quantum evolution equatio ns reproduce the correct Langevin dynamics in the semiclassical limit. The consequences for the issues of decoherence and localization are d iscussed.