Non-adiabatic transitions in the condensed phase. Derivation of multichannel Fokker-Planck equations from quantum relaxation theory

A new formalism is proposed for the derivation of multichannel Fokker-Planck equations describing reactive processes in the condensed phase. It is based upon the method of quantum-classical reduction for the dynamical and relaxation parts of the general equation of quantum relaxation theory. In this way, the multilevel non-Markov Fokker-Planck and Smoluchovsky-type equations are obtained taking into account the non-adiabatic dynamics of the system. These equations include memory effects with a generalization of the non-local relaxation kernel beyond the high-temperature approximation. The formulation of the balance equations describing the kinetics of non-adiabatic reactions in polar solvents is examined and the prospects of deriving corresponding rate expressions are discussed.