Monte Carlo generation of localised particle trajectories
Abstract
We introduce modifications to Monte Carlo simulations of the Feynman path integral that improve sampling of localised interactions. The new algorithms generate trajectories in simple background potentials designed to concentrate them about the interaction region, reminiscent of importance sampling. This improves statistical sampling of the system and overcomes a long-time "undersampling problem" caused by the spatial diffusion inherent in Brownian motion. We prove the validity of our approach using previous analytic work on the distribution of values of the Wilson line over path integral trajectories and illustrate the improvements on some simple quantum mechanical systems
Keywords
Cite
@article{arxiv.2304.10518,
title = {Monte Carlo generation of localised particle trajectories},
author = {Ivan Ahumada and James P. Edwards},
journal= {arXiv preprint arXiv:2304.10518},
year = {2025}
}
Comments
8 pages plus 3 appendices, various figures. The article has been accepted in Physical Review E