Dimension-free Ergodicity of Path Integral Molecular Dynamics

• URL: http://arxiv.org/abs/2307.06510v4
• Date: Sun, 23 Jun 2024 07:35:57 GMT
• Title: Dimension-free Ergodicity of Path Integral Molecular Dynamics
• Abstract summary: Path integral molecular dynamics is a prevailing approach for computing quantum thermal averages. We study the Matsubara mode PIMD, where the ring polymer is replaced by a continuous loop composed of $N$ Matsubara modes. We prove that both the Matsubara mode PIMD and the standard PIMD have uniform-in-$N$ ergodicity.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $N$.

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