Work

Dimension-Free Ergodicity of Path Integral Molecular Dynamics

Year: 2025

Type: article

Abstract: 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 $N$.

Source: Communications in Computational Physics

DOI: 10.4208/cicp.oa-2024-0004

Authors: Xuda Ye, Zhennan Zhou

Institutions: Peking University, Westlake University

Language: English

Topic: Quantum, superfluid, helium dynamics

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Natural Science Foundation of China, Shanghai Jiao Tong University, Peking University

Awards: G4517293849, G7627071985