On the Schrödinger-Langevin picture and the master equation

The temperature-dependent quantum master equation is derived by generalizing van Kampenʹs method. Starting with a stochastic Schrödinger equation and taking into account the finite quantum correlation-time of the thermal bath, we have found a fluctuation-dissipation-like relation. The normalization and the Hermitian property of the reduced density matrix are guaranteed. To the lowest order of the Kubo number, a temperature-dependent Kossakowski-Lindblad map is found. A particular system is solved: the harmonic oscillator in interaction with a thermal bath of oscillators. The classical limit is also discussed. We have stressed the usefulness of this Schrödinger-Langevin picture to study nonequilibrium many-body quantum statistical mechanic systems. The possibility to go beyond the Markovian map is stressed.