Overlapping Resonances in Open Quantum Systems

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/σ2. We give a detailed expansion of the system-reservoir evolution showing the above scenario. 1 Introduction and main results We consider an open quantum system consisting of a small, finite-dimensional part in-teracting with a heat bath, modeled by a spatially infinitely extended free Bose gas in thermal equilibrium. The analysis of such systems, and especially of their dynamics, ha