TY - JOUR
T1 - Dimension-Free Ergodicity of Path Integral  Molecular Dynamics
AU - Ye , Xuda
AU - Zhou , Zhennan
JO - Communications in Computational Physics
VL - 5
SP - 1355
EP - 1388
PY - 2025
DA - 2025/09
SN - 38
DO - http://doi.org/10.4208/cicp.OA-2024-0004
UR - https://global-sci.org/intro/article_detail/cicp/24460.html
KW - Quantum thermal average, path integral molecular dynamics, Matsubara modes, ergodicity, generalized $\Gamma$ calculus.
AB - <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>