Abstract
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.
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