Quantum Master Equation of a Particle in a Gas Environment

The evolution of the reduced density operator \ 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 \ local environmental interactions. We derive a Lindblad master equation for \, whose generators are calculated from differential cross section of a single collision between Brownian and gas particles, respectively. The existence of thermal equilibrium for \ is proved. Master equations proposed earlier are shown to be particular cases of our one.