Strong-damping limit of quantum Brownian motion in a disordered environment

TL;DR

This paper analyzes how a quantum system coupled to a disordered environment exhibits non-Gaussian Markovian noise in the strong damping limit, revealing complex diffusion behavior and steady-state properties.

Contribution

It introduces a microscopic model showing that finite bath correlation length causes non-Gaussian noise in the overdamped quantum regime and provides analytical solutions for a harmonic oscillator.

Findings

Position distribution follows a generalized Kramers-Moyal equation with infinite derivatives.

The noise is non-Gaussian due to finite bath correlation length.

Steady-state properties of the system are analytically characterized.

Abstract

We consider a microscopic model of an inhomogeneous environment where an arbitrary quantum system is locally coupled to a harmonic bath via a finite-range interaction. We show that in the overdamped regime the position distribution obeys a classical Kramers-Moyal equation that involves an infinite number of higher derivatives, implying that the finite bath correlation length leads to non-Gaussian Markovian noise. We analytically solve the equation for a harmonically bound particle and analyze its non-Gaussian diffusion as well as its steady-state properties.