Exact Volterra series for mean field dynamics
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909986015150080 |
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| author | Santra, Ion Krüger, Matthias |
| author_facet | Santra, Ion Krüger, Matthias |
| contents | We derive an exact Volterra series expansion for a mean field of an interacting particle system subject to a potential perturbation, expressing the Volterra expansion kernels in terms of the field's response functions, to any order. Applying this formalism to the mean particle density of a simple fluid, we identify a form reminiscent of dynamical density functional theory, with, however, fundamental differences: A nonlocal mobility kernel appears, and forces derive from a functional of the {\it history} of mean density. The equilibrium density functional is shown to be recovered in the limit of slowly varying perturbation. We identify a freedom in deriving this expansion, which allows different forms of mobility kernels. These developments allow for a systematic improvement of established mean field formalisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06004 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact Volterra series for mean field dynamics Santra, Ion Krüger, Matthias Statistical Mechanics We derive an exact Volterra series expansion for a mean field of an interacting particle system subject to a potential perturbation, expressing the Volterra expansion kernels in terms of the field's response functions, to any order. Applying this formalism to the mean particle density of a simple fluid, we identify a form reminiscent of dynamical density functional theory, with, however, fundamental differences: A nonlocal mobility kernel appears, and forces derive from a functional of the {\it history} of mean density. The equilibrium density functional is shown to be recovered in the limit of slowly varying perturbation. We identify a freedom in deriving this expansion, which allows different forms of mobility kernels. These developments allow for a systematic improvement of established mean field formalisms. |
| title | Exact Volterra series for mean field dynamics |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2601.06004 |