MONTE-CARLO EVALUATION OF REAL-TIME FEYNMAN PATH-INTEGRALS FOR QUANTAL MANY-BODY DYNAMICS - DISTRIBUTED APPROXIMATING FUNCTIONS AND GAUSSIAN SAMPLING

In this paper we report the initial steps in the development of a Monte Carlo method for evaluation of real-time Feynman path integrals for many-particle dynamics. The approach leads to Gaussian importance sampling for real-time dynamics in which the sampling function is short ranged due to the occurrence of Gaussian factors. These Gaussian factors result from the use of a generalization of our new discrete distributed approximating functions (DDAFs) to continuous distributed approximating functions (CDAFs) so as to replace the exact coordinate representation free-particle propagator by a "CDAF-class, free-particle propagator" which is highly banded. The envelope of the CDAF-class free propagator is the product of a "bare Gaussian", exp[-(x'- x)2sigma2(0)/(2sigma4(0) + H2tau2/m2BAR)], with a "shape polynomial" in (x' - x)2, where sigma(0) is a width parameter at zero time (associated with the description of the wavepacket in terms of Hermite functions), tau is the time step (tau = t/N, where t is the total propagation time), and x and x' are any two configurations of the system. The bare Gaussians are used for Monte Carlo integration of a path integral for the survival probability of a Gaussian wavepacket in a Morse potential. The approach appears promising for real-time quantum Monte Carlo studies based on the time-dependent Schrodinger equation, the time-dependent von Neumann equation, and related equations.