Kinetic description of quantum Brownian motion

TL;DR

This paper emphasizes the importance of translational invariance and atomic gas nature in quantum Brownian motion, deriving a Lindblad-form master equation that respects translation covariance.

Contribution

It introduces a quantum master equation for Brownian motion that incorporates translational invariance and atomic gas features, aligning with Einstein's classical picture.

Findings

Master equation of Lindblad form derived

Ensures covariance under translations

Highlights the role of atomic gas nature

Abstract

We stress the relevance of the two features of translational invariance and atomic nature of the gas in the quantum description of the motion of a massive test particle in a gas, corresponding to the original picture of Einstein used in the characterization of Brownian motion. The master equation describing the reduced dynamics of the test particle is of Lindblad form and complies with the requirement of covariance under translations.