Evolution equations for the average energy of a harmonic oscillator in interaction with a bath are derived and solved for two cases: (a) when the probability evolution obeys a master equation with a true decay representing a sink-process like radiative emission occurring simultaneously with vibrational relaxation, and (b) when the Markoffian approximation in the Heisenberg-equation analysis of relaxation is not made, allowing for short-time effects.
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Kenkre et al. (1977) studied this question.
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