Fast sampling algorithm for Lie-Trotter products.
A fast algorithm for path sampling in path-integral Monte Carlo simulations is proposed. The algorithm utilizes the Lévy-Ciesielski implementation of Lie-Trotter products to achieve a mathematically proven computational cost of n log2(n) with the number of time slices n, despite the fact that each path variable is updated separately, for reasons of optimality. In this respect, we demonstrate that updating a group of random variables simultaneously results in loss of efficiency.
Predescu
Cristian
C
Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720, USA. cpredescu@comcast.net