QUANTUM FOKKER-PLANCK THEORY IN A NON-GAUSSIAN-MARKOVIAN MEDIUM

We develop a generalized quantum Fokker-Planck theory in a non-Gaussia n-Markovian model bath. The semiclassical bath adopted in this work is charactered by three parameters. One denotes the strength of system-b ath coupling and the other two are chosen to interpolate smoothly the solvation dynamics between the long- and short-time regimes. The fluct uation-dissipation relation in this model bath is analyzed in detail. Based on this model bath, we derive two sets of coupled Fokker-Planck equations. These two equation sets are equivalent in the second order of system-bath coupling but different in the higher orders. The corres ponding reduced Liouville equation in one set of the Fokker-Planck for mulation is characterized by a memory relaxation kernel, while that in the other is by a local-time relaxation tensor. Each resulting set of Fokker-Planck equations involves only the reduced density operator an d a series of well-characterized Hilbert-space relaxation operators. T he present theory is valid for arbitrary time-dependent Hamiltonians a nd is applicable to the study of quantum coherence and relaxation in v arious dynamic systems. [S1050-2947(98)05210-X].