Quantum generalized Langevin equation: Explicit inclusion of nonlinear system dynamics

Abstract

We derive a quantum nonlinear generalized Langevin equation (GLE) which includes system anharmonic and nonlinear effects explicitly through either gas phase potentials or potentials of mean force. The GLE is applicable to a broad class of nonlinear Hamiltonians with time reversal invariance being the principal restriction. The constraint of linear coupling of the system to the bath is removed. Molecular time scale generalized Langevin equation theory (MTGLE) emerges as the limit case when the nonlinearities are removed explicitly from the system. Specifically, the usual harmonic approach to the dynamics of the MTGLE primary zone (or system in a system/bath partitioning) is replaced by a more general approach which allows for anharmonic and nonlinear effects. Appropriate statistical averages are developed which permit averaging over the bath and a reduction of the number of degrees of freedom to those present in the system. The final form of the quantum nonlinear GLE with attendant statistical relations is...