Classical and quantum dissipation in non homogeneous environments

TL;DR

This paper extends the oscillator model to include nonlinear couplings and space-time dependent bath oscillators, providing a unified framework for classical and quantum dissipation in nonhomogeneous environments, with implications for decoherence.

Contribution

It introduces a generalized model with nonlinear and space-time dependent bath oscillators, deriving new equations for classical and quantum dissipation in complex environments.

Findings

Derived a generalized Langevin equation with nonlinear multiplicative noise.

Predicted a new force term in time-modulated noise scenarios.

Reproduced correct semiclassical Langevin dynamics in the quantum model.

Abstract

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.