IMPROVED FEYNMAN PATH-INTEGRAL METHOD WITH A LARGE TIME-STEP - FORMALISM AND APPLICATIONS

We describe an efficient path integral scheme for calculating the prop agator of an arbitrary quantum system, as well as that of a stochastic system in special cases where the Fokker-Planck equation obeys strict detailed balance. The basic idea is to split the respective Hamiltoni an into two exactly solvable parts and then to employ a symmetric deco mposition of the time evolution operator, which is exact up to a high order in the time step. The resulting single step propagator allows ra ther large time steps in a path integral and leads to convergence with fewer time slices. Because it involves no system-specific reference s ystem, the algorithm is amenable to all known numerical schemes availa ble for evaluating quantum path integrals. In this way one obtains a h ighly accurate method, which is simultaneously fast, stable, and compu tationally simple. Numerical applications to the real time quantum dyn amics in a double well and to the stochastic dynamics of a bistable sy stem coupled to a harmonic mode show our method to be superior over th e approach developed by the Makri group in their quasiadiabatic propag ator representation, to say nothing about the propagation scheme based on the standard Trotter splitting. (C) 1998 American Institute of Phy sics.