Quantum Master Equation of Particle in Gas Environment

TL;DR

This paper derives a Lindblad master equation describing the quantum evolution of a Brownian particle in a low-density gas, establishing the first successful quantum friction model from local environmental interactions.

Contribution

It presents the first derivation of a quantum friction master equation based on local collisions, connecting microscopic cross sections to the quantum dynamics.

Findings

Derived a Lindblad master equation from collision cross sections

Proved the existence of thermal equilibrium for the system

Unified previous models as special cases of the new equation

Abstract

The evolution of the reduced density operator $\rho$ of Brownian particle is discussed in single collision approach valid typically in low density gas environments. This is the first succesful derivation of quantum friction caused by {\it local} environmental interactions. We derive a Lindblad master equation for $\rho$, whose generators are calculated from differential cross section of a single collision between Brownian and gas particles, respectively. The existence of thermal equilibrium for $\rho$ is proved. Master equations proposed earlier are shown to be particular cases of our one.