Time-dependent transition rates for a multilevel quantum system interacting with a bath lacking a characteristic relaxation time

This work presents a semiclassical calculation for the time-dependent transition rates (TDTR's) of a multilevel quantum system interacting with a reservoir characterized by a power-law distribution of relaxation times. Some simple asymptotic expressions for these TDTR's are given, which can be very useful in order to be used in non-Markovian master equations.