Quantum Master Equation of Particle in Gas Environment

Abstract

The evolution of the reduced density operator $ρ$ 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 $ρ$, whose generators are calculated from differential cross section of a single collision between Brownian and gas particles, respectively. The existence of thermal equilibrium for $ρ$ is proved. Master equations proposed earlier are shown to be particular cases of our one.