We consider systems coupled to a heat reservoir that has a Debye density of states. In particular, starting from master equations derived in the secular (or rotating-wave) approximation, we derive expressions for the decoherence rates and energy-jump moments for systems and couplings of varying degrees of generality. We also furnish the semiclassical analogs of these expressions. Finally, using the jump moments, we examine various aspects of the energy relaxation to thermal equilibrium.

• Received 26 May 1993

DOI:https://doi.org/10.1103/PhysRevA.49.89