On Diffusion Monte Carlo in spaces with multi-valued maps, boundaries and gradient torsion

Abstract

Importance sampling in Diffusion Monte Carlo has a long history. However, only recently, simulations of ground state properties have been extended to spaces mapped with non-Cartesian coordinates. We demonstrate that in spaces with nonzero advection the Smoluchowski operator for any nontrivial trial wavefunction does not converge to the exact result. Rather, every drift term is equivalent to some advection in a manifold that contains the physical space of the system. Since these manifolds may be formulated with gradient torsion we demonstrate with several numerical experiments that Diffusion Monte Carlo is possible in these as well.