Memory propagator matrix for long-time dissipative charge transfer dynamics

Abstract

Iterative path integral methods provide a numerically exact approach to the dynamics of a quantum system coupled to a dissipative bath. These methods involve step-by-step propagation of a generalized multi-time reduced density matrix with a propagator that includes influence functional interactions that span the bath-induced memory length. Low-frequency baths lead to long memory that can span many time steps, necessitating the use of filtering procedures that select and store only statistically significant path segments, avoiding storage of the entire sparse propagator. The present paper further enhances the iterative path integral methodology through a deterministic procedure that identifies at the start of the calculation all memory-length path segments whose weights exceed a chosen threshold and builds the propagator matrix for use in all propagation steps. A binning procedure allows efficient pairing of path segments required in the construction of the propagator. Additional savings are achieved via a simple criterion for assessing the adequacy of a chosen path selection threshold prior to propagation. Application to a tight-binding model for charge transfer in extended systems reveals the important role of bath-induced memory on the dynamics of these systems.