Continuous path brownian trajectories for diffusion monte carlo via first- and last-passage distributions

Abstract

This paper provides a review of a new method of addressingproblems in diffusion Monte Carlo: the Green’s function first-passagemethod (GFFP). In particular, we address three new strands of thoughtand their interaction with the GFFP method: the use of angle-averagingmethods to reduce vector or tensor Laplace equations to scalar Laplaceequations; the use of the simulation-tabulation (ST) method to dramaticallyexpand the range of the GFFP method; and the development oflast-passage diffusion methods; these drastically improve the efficiencyof diffusion Monte Carlo methods. All of these claims are addressed indetail, with specific examples.