On the Schrödinger-Langevin picture and the master equation

Manuel O. Cáceres and Ana K. Chattah

Physica A: Statistical Mechanics and its Applications, 1996, vol. 234, issue 1, 322-340

Abstract: The temperature-dependent quantum master equation is derived by generalizing van Kampen's 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.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:234:y:1996:i:1:p:322-340

DOI: 10.1016/S0378-4371(96)00263-4

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