  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.
