Abstract
An N-level quantum system is coupled to a bosonic heat reservoir at positive temperature. We analyze the system–reservoir dynamics in the following regime: the strength λ of the system–reservoir coupling is fixed and small, but larger than the spacing σ of system energy levels. For vanishing σ there is a manifold of invariant system–reservoir states and for σ > 0 the only invariant state is the joint equilibrium. The manifold is invariant for σ = 0 but becomes quasi-invariant for σ > 0. Namely, on a first time-scale of the order 1/λ2, initial states approach the manifold. Then, they converge to the joint equilibrium state on a much larger time-scale of the order λ2/σ 2. We give a detailed expansion of the system–reservoir evolution showing the above scenario.
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Communicated by Claude Alain Pillet.
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Merkli, M., Song, H. Overlapping Resonances in Open Quantum Systems. Ann. Henri Poincaré 16, 1397–1427 (2015). https://doi.org/10.1007/s00023-014-0349-x
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DOI: https://doi.org/10.1007/s00023-014-0349-x