Exact Non-Markovian Evolution with Several Reservoirs

The model of a multilevel system interacting with several reservoirs is considered. The exact reduced evolution of a system’s density matrix can be obtained for this model without using the Markov approximation. Namely, this evolution is completely defined by the finite set of linear differential equations. The results obtained earlier for one Lorentz peak in the spectral density are generalized to the case of an arbitrary number of such peaks. The contribution of Ohmic spectral density is also considered.