@Article{CiCP-38-1355,
author = {Ye , Xuda and Zhou , Zhennan},
title = {Dimension-Free Ergodicity of Path Integral  Molecular Dynamics},
journal = {Communications in Computational Physics},
year = {2025},
volume = {38},
number = {5},
pages = {1355--1388},
abstract = {<p style="text-align: justify;">The quantum thermal average plays a central role in describing the thermodynamic properties of a quantum system. Path integral molecular dynamics (PIMD)
 is a prevailing approach for computing quantum thermal averages by approximating
 the quantum partition function as a classical isomorphism on an augmented space, enabling efficient classical sampling, but the theoretical knowledge of the ergodicity of
 the sampling is lacking. Parallel to the standard PIMD with $N$ ring polymer beads, we
 also study the Matsubara mode PIMD, where the ring polymer is replaced by a continuous loop composed of $N$ Matsubara modes. Utilizing the generalized $\Gamma$ calculus,
 we prove that both the Matsubara mode PIMD and the standard PIMD have uniform-in-$N$ ergodicity, i.e., the convergence rate towards the invariant distribution does not
 depend on the number of modes or beads $N$.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2024-0004},
url = {http://global-sci.org/intro/article_detail/cicp/24460.html}
}