Effective classical potential for quantum statistical averages
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912903282556928 |
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| author | Sadhasivam, Vijay Ganesh Althorpe, Stuart C. Kapil, Venkat |
| author_facet | Sadhasivam, Vijay Ganesh Althorpe, Stuart C. Kapil, Venkat |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13006 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Effective classical potential for quantum statistical averages Sadhasivam, Vijay Ganesh Althorpe, Stuart C. Kapil, Venkat Quantum Physics Chemical Physics 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. |
| title | Effective classical potential for quantum statistical averages |
| topic | Quantum Physics Chemical Physics |
| url | https://arxiv.org/abs/2602.13006 |