  We generalize the oscillator model of a particle interacting with a thermal
reservoir by introducing arbitrary nonlinear couplings in the particle
coordinates.The equilibrium positions of the heat bath oscillators are promoted
to space-time functions, which are shown to represent a modulation of the
internal noise by the external forces. The model thus provides a description of
classical and quantum dissipation in non homogeneous environments. In the
classical case we derive a generalized Langevin equation with nonlinear
multiplicative noise and a position-dependent fluctuation- dissipation theorem
associated to non homogeneous dissipative forces. When time-modulation of the
noise is present, a new force term is predicted besides the dissipative and
random ones. The model is quantized to obtain the non homogenous influence
functional and master equation for the reduced density matrix of the Brownian
particle. The quantum evolution equations reproduce the correct Langevin
dynamics in the semiclassical limit. The consequences for the issues of
decoherence and localization are discussed.
