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This paper presents a novel mathematical reformulation of the Feynman path integral using Gaussian sampling, specifically targeting improvements in quantum Monte Carlo simulations for statistical mechanics. By deriving variance and mean from ring polymer statistics rather than relying on multiple temperature nodes, this approach addresses numerical cancellation issues that plague conventional methods. The study validates its efficacy through analytic calculations and simulations comparing helium's second virial coefficient against laboratory data.
Gaussian Reformulation of the Feynman Path Integral for Quantum Statistical Mechanics with Results for the Second Virial Coefficient of $^4$He
arXiv:2607.16301v1 Announce Type: cross Abstract: The Feynman path integral for quantum statistical mechanics is reformulated as Gaussian sampling of the neighborhood of each position configuration. The variance and mean are obtained from ring polymer statistics on a lattice, and from the high temperature expansion of the Wigner-Kirkwood commutation function, respectively. The algorithm avoids multiple temperature nodes for each configuration and the need for numerical cancelation in the statistical averages, which are problematic for conventional path integral quantum Monte Carlo. Analytic and simulation results for the second virial coefficient of helium are compared to laboratory measurements.
Abstract:The Feynman path integral for quantum statistical mechanics is reformulated as Gaussian sampling of the neighborhood of each position configuration. The variance and mean are obtained from ring polymer statistics on a lattice, and from the high temperature expansion of the Wigner-Kirkwood commutation function, respectively. The algorithm avoids multiple temperature nodes for each configuration and the need for numerical cancelation in the statistical averages, which are problematic for conventional path integral quantum Monte Carlo. Analytic and simulation results for the second virial coefficient of helium are compared to laboratory measurements.
Statistical Mechanics (cond-mat.stat-mech); Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
arXiv:2607.16301 [cond-mat.stat-mech]
(or arXiv:2607.16301v1 [cond-mat.stat-mech] for this version)
https://doi.org/10.48550/arXiv.2607.16301 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 188 words
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