Cluster expansions of particle system state with topological nearest-neighbor interaction
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915695618424832 |
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| author | Gerasimenko, V. I. Gapyak, I. V. |
| author_facet | Gerasimenko, V. I. Gapyak, I. V. |
| contents | The article presents the concept of a cumulant representation for distribution functions describing the states of many-particle systems with topological nearest-neighbor interaction. A solution to the Cauchy problem for the hierarchy of nonlinear evolution equations for the cumulants of distribution functions of such systems is constructed. The connection between the constructed solution and the series expansion structure for a solution to the Cauchy problem of the BBGKY hierarchy has been established. Furthermore, the expansion structure for a solution to the Cauchy problem of the hierarchy of evolution equations for reduced observables of topologically interacting particles is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08412 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cluster expansions of particle system state with topological nearest-neighbor interaction Gerasimenko, V. I. Gapyak, I. V. Mathematical Physics Statistical Mechanics Analysis of PDEs Dynamical Systems 35C10, 35Q20, 82C05, 82D05, 70F45 The article presents the concept of a cumulant representation for distribution functions describing the states of many-particle systems with topological nearest-neighbor interaction. A solution to the Cauchy problem for the hierarchy of nonlinear evolution equations for the cumulants of distribution functions of such systems is constructed. The connection between the constructed solution and the series expansion structure for a solution to the Cauchy problem of the BBGKY hierarchy has been established. Furthermore, the expansion structure for a solution to the Cauchy problem of the hierarchy of evolution equations for reduced observables of topologically interacting particles is established. |
| title | Cluster expansions of particle system state with topological nearest-neighbor interaction |
| topic | Mathematical Physics Statistical Mechanics Analysis of PDEs Dynamical Systems 35C10, 35Q20, 82C05, 82D05, 70F45 |
| url | https://arxiv.org/abs/2503.08412 |