(untitled) (Communications in Computational Physics, 2025)
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 Γ 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.