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  • Open Access

Effective classical potential for quantum statistical averages

Vijay Ganesh Sadhasivam1, Stuart C. Althorpe1, and Venkat Kapil1,2,3,*

  • *Contact author: v.kapil@ucl.ac.uk
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Phys. Rev. E 114, 024126 – Published 14 August, 2026

DOI: https://doi.org/10.1103/zr37-gtc5

Abstract

We present an effective potential that allows quantum thermal expectation values of a position-dependent observable to be estimated as a classical ensemble average of the corresponding function. We follow the approach of Feynman and Hibbs but perform the mean-field treatment of quantum fluctuations about the path starting point rather than the path centroid. Furthermore, rather than performing a full variational optimization of the potential, we explore approximate functional forms that yield numerical robustness. The resulting closed-form potential is exact in the classical and harmonic limits; benchmarks against exact position distributions for one-dimensional quartic, Morse, and double-well potentials show good agreement for potentials with harmonic support.

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Phys. Rev. E 114, 024126– Published 14 August, 2026
  • Received 13 February 2026
  • Accepted 10 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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