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On the Schrödinger-Langevin picture and the master equation

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  • Cáceres, Manuel O.
  • Chattah, Ana K.

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.

Suggested Citation

  • Cáceres, Manuel O. & Chattah, Ana K., 1996. "On the Schrödinger-Langevin picture and the master equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 234(1), pages 322-340.
    • Handle: RePEc:eee:phsmap:v:234:y:1996:i:1:p:322-340
    DOI: 10.1016/S0378-4371(96)00263-4
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    1. Micheline Thomine-Desmazures, 1965. "L'investigation psychosociologique en milieu rural," Économie rurale, Programme National Persée, vol. 64(1), pages 19-24.
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