Mean-field evolution of open quantum systems: an exactly solvable model | Zendy

Marco Merkli | Zendy; G. P. Berman | Zendy

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Mean-field evolution of open quantum systems: an exactly solvable model

Author(s) -

Marco Merkli,

G. P. Berman

Publication year - 2012

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2012.0327

Subject(s) - dissipative system , physics , lindblad equation , coupling (piping) , quantum , master equation , nonlinear system , statistical physics , limit (mathematics) , field (mathematics) , quantum field theory , mean field theory , coupling constant , quantum mechanics , open quantum system , classical mechanics , mathematics , mathematical analysis , mechanical engineering , pure mathematics , engineering

We consider quantum particles coupled to local and collective thermal quantum environments. The coupling is energy conserving, and the collective coupling is scaled in the mean-field way. There is no direct interaction between the particles. We show that an initially factorized state of the particles remains factorized at all times, in the limit of large particle number. Each single-particle factor evolves according to an explicit, nonlinear, dissipative and time-dependent Hartree–Lindblad equation. The model is exactly solvable; we do not make any weak coupling or any Markovian approximations, and our results are mathematically rigorous.

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