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Mixing properties of the one-atom maser

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Abstract

We study the relaxation properties of the quantized electromagnetic field in a cavity under repeated interactions with single two-level atoms, so-called one-atom maser. We improve the ergodic results obtained in Bruneau and Pillet (J Stat Phys 134(5–6):1071–1095, 2009) and prove that, whenever the atoms are initially distributed according to the canonical ensemble at temperature \(T>0\), all the invariant states are mixing. Under some non-resonance condition this invariant state is known to be thermal equilibirum at some renormalized temperature \(T^*\) and we prove that the mixing is then arbitrarily slow, in other words that there is no lower bound on the relaxation speed.

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Notes

  1. \(c_0\) denotes the Banach space of complex sequences which converge to \(0\) (endowed with the \(\ell ^\infty \) norm).

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Acknowledgments

The author is grateful to V. Georgescu for fruitful discussions and to C. Pellegrini for drawing his attention to reference [21]. This work was partially supported by the Agence Nationale de la Recherche, grant ANR-09-BLAN-0098-01.

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

    Laurent Bruneau

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Correspondence to Laurent Bruneau.

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Bruneau, L. Mixing properties of the one-atom maser. J Stat Phys 155, 888–908 (2014). https://doi.org/10.1007/s10955-014-0982-2

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