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 lambda of the system-reservoir coupling is fixed and small, but larger than the spacing sigma of system energy levels. For vanishing sigma there is a manifold of invariant system-reservoir states and for sigma > 0 the only invariant state is the joint equilibrium. The manifold is invariant for sigma = 0 but becomes quasi-invariant for sigma > 0. Namely, on a first time-scale of the order 1/lambda(2), initial states approach the manifold. Then, they converge to the joint equilibrium state on a much larger time-scale of the order lambda(2)/sigma (2). We give a detailed expansion of the system-reservoir evolution showing the above scenario.