| Abstract: |
| Path integral molecular dynamics (PIMD) is a standard method for computing thermal averages in quantum canonical ensembles, with its accuracy depending on the number of beads, $D$, representing the discretization size of the Feynman path integral. Despite its widespread use in computational physics, the ergodicity of PIMD, particularly the dependence of the convergence rate on $D$, is not well understood. In this talk, I will present a rigorous analysis proving the uniform-in-$D$ ergodicity of PIMD, meaning that the convergence rate toward equilibrium is independent of the bead count $D$. This result is established for both overdamped and underdamped Langevin dynamics. Our approach relies on the generalized Gamma calculus, an advanced technique related to hypocoercivity, developed by Pierre Monmarch\`{e}, which provides deeper insight into the long-time behavior of these stochastic systems. |
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