Master Equation for a Quantum Particle in a Gas

The equation for the quantum motion of a Brownian particle in a gaseous environment is derived by means of $S$-matrix theory. This quantum version of the linear Boltzmann equation accounts nonperturbatively for the quantum effects of the scattering dynamics and describes decoherence and dissipation in a unified framework. As a completely positive master equation it incorporates both the known equation for an infinitely massive Brownian particle and the classical linear Boltzmann equation as limiting cases.