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Thermal Relaxation of a QED Cavity

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Abstract

We study repeated interactions of the quantized electromagnetic field in a cavity with single two-levels atoms. Using the Markovian nature of the resulting quantum evolution we study its large time asymptotics. We show that, whenever the atoms are distributed according to the canonical ensemble at temperature T>0 and some generic non-degeneracy condition is satisfied, the cavity field relaxes towards some invariant state. Under some more stringent non-resonance condition, this invariant state is thermal equilibrium at some renormalized temperature T *. Our result is non-perturbative in the strength of the atom-field coupling. The relaxation process is slow (non-exponential) due to the presence of infinitely many metastable states of the cavity field.

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Authors and Affiliations

  1. CNRS-UMR 8088 et Département de Mathématiques, Université de Cergy-Pontoise, Site Saint-Martin, BP 222, 95302, Cergy-Pontoise, France

    L. Bruneau

  2. Centre de Physique Théorique (CNRS, Université de Provence, Université de la Méditerranée, Université de Toulon) – UMR 6207, Université du Sud, Toulon–Var, BP 20132, 83957, La Garde Cedex, France

    C.-A. Pillet

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  1. L. Bruneau
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Correspondence to C.-A. Pillet.

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Dedicated to Jürg Fröhlich and Thomas Spencer on the occasion of their 60th birthday.

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Bruneau, L., Pillet, CA. Thermal Relaxation of a QED Cavity. J Stat Phys 134, 1071–1095 (2009). https://doi.org/10.1007/s10955-008-9656-2

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