Quantum Master Equation of a Particle in a Gas Environment

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 {\ 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.