Effective classical potential for quantum statistical averages
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 a 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.
Keywords
Cite
@article{arxiv.2602.13006,
title = {Effective classical potential for quantum statistical averages},
author = {Vijay Ganesh Sadhasivam and Stuart C. Althorpe and Venkat Kapil},
journal= {arXiv preprint arXiv:2602.13006},
year = {2026}
}