Path integrals for dissipative systems by tensor multiplication. Condensed phase quantum dynamics for arbitrarily long time

Feynman's influence functional that arises from many-particle environments is nonlocal in time but the nonlocality has finite range, even at very low temperature. Use of our numerically constructed quasi-adiabatic propagators permits large time steps in the path integral, such that the nonlocality of the influence functional spans only a few time steps. We exploit these observations to propose an iterative scheme for the evaluation of path integrals by stepwise multiplication of a propagator tensor, thereby making exact quantum dynamics calculations in condensed phase systems feasible for arbitrarily long times.