A Lindblad Model of Quantum Brownian Motion

TL;DR

This paper develops a Lindblad-form quantum Brownian motion model that maintains positivity of the density operator at low temperatures, providing a more accurate description of open quantum systems and their environment-induced properties.

Contribution

It introduces an extended Lindblad model for quantum Brownian motion that overcomes positivity issues present in traditional models at low temperatures.

Findings

The model accurately describes stationary states of quantum Brownian motion.

It reveals how environment-induced correlations and squeezing depend on coupling.

The approach ensures physical consistency at all temperatures.

Abstract

The theory of quantum Brownian motion describes the properties of a large class of open quantum systems. Nonetheless, its description in terms of a Born-Markov master equation, widely used in the literature, is known to violate the positivity of the density operator at very low temperatures. We study an extension of existing models, leading to an equation in the Lindblad form, which is free of this problem. We study the dynamics of the model, including the detailed properties of its stationary solution, for both constant and position-dependent coupling of the Brownian particle to the bath, focusing in particular on the correlations and the squeezing of the probability distribution induced by the environment