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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2307.06510 |
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| _version_ | 1866916298153263104 |
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| author | Ye, Xuda Zhou, Zhennan |
| author_facet | Ye, Xuda Zhou, Zhennan |
| contents | 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 $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06510 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dimension-free Ergodicity of Path Integral Molecular Dynamics Ye, Xuda Zhou, Zhennan Numerical Analysis Probability Computational Physics Quantum Physics 37A30, 82B31, 81S40 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 $N$. |
| title | Dimension-free Ergodicity of Path Integral Molecular Dynamics |
| topic | Numerical Analysis Probability Computational Physics Quantum Physics 37A30, 82B31, 81S40 |
| url | https://arxiv.org/abs/2307.06510 |