Abstract
The heat-bath frequency distribution, necessary to maintain the canonical commutation relations for all time for a quantum mechanical oscillator with non-Markovian features like memory-dependent damping, is shown to satisfy certain constraint relations. An algorithm is given to explicitly find the heat-bath frequency distribution in terms of a series expansion for all processes where the timescale for the non-Markovian memory kernel is much smaller than the inverse of the strength of damping term. In the non-Markovian case, the heat-bath distribution function exhibits dependence on the system characteristics. The KS periodicity conditions on the system Green functions as the system approaches equilibrium are established for the present case.
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