The fast sampling algorithm for Lie-Trotter products
Abstract
A fast algorithm for path sampling in path integral Monte Carlo simulations is proposed. The algorithm utilizes the Levy-Ciesielski implementation of Lie-Trotter products to achieve a mathematically proven computational cost of n*log_2(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.
Keywords
Cite
@article{arxiv.cond-mat/0411048,
title = {The fast sampling algorithm for Lie-Trotter products},
author = {Cristian Predescu},
journal= {arXiv preprint arXiv:cond-mat/0411048},
year = {2009}
}
Comments
4 pages, 1 figure; fast rejection from Phys. Rev. Letts; transfered to PRE as a Rapid Communication. Eq. 6 to 10 contained some inconsistencies that have been repaired in the present version; A sample code implementing the algorithm for LJ clusters is available from the author upon request