Self-adaptive quadrature and numerical path integration

Abstract

The role of the choice of numerical quadrature on the convergence properties of numerical path integration algorithms is discussed. It shown that, for restricted class of interaction potentials, Gauss moment methods are feasible. These self-adaptive, coordinate-domain methods break free of the limits on the convergence rates of quadrature error otherwise imposed by fixed, time-domain quadrature. When applicable, these methods appear to reduce the number of evaluations of the potential energy required for typical numerical path integral applications.