Quantum state-dependent diffusion and multiplicative noise: a microscopic approach

TL;DR

This paper develops a microscopic quantum model for state-dependent diffusion and multiplicative noise, deriving a Langevin and Fokker-Planck framework, and explores quantum currents arising from inhomogeneous media.

Contribution

It introduces a quantum microscopic approach to state-dependent diffusion using a nonlinear system-reservoir coupling model, extending classical concepts into the quantum domain.

Findings

Derived a quantum Langevin equation for inhomogeneous media

Formulated a Fokker-Planck equation in position space

Identified conditions for observing quantum currents

Abstract

The state-dependent diffusion, which concerns the Brownian motion of a particle in inhomogeneous media has been described phenomenologically in a number of ways. Based on a system-reservoir nonlinear coupling model we present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Markovian Langevin description and an associated Fokker-Planck equation in position space in the overdamped limit. We examine the thermodynamic consistency and explore the possibility of observing a quantum current, a generic quantum effect, as a consequence of this state-dependent diffusion similar to one proposed by B\"{u}ttiker [Z. Phys. B {\bf 68}, 161 (1987)] in a classical context several years ago.