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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.14875 |
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| _version_ | 1866915471906832384 |
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| author | Krapivsky, P. L. Mallick, Kirone |
| author_facet | Krapivsky, P. L. Mallick, Kirone |
| contents | We study the evolution of a system of many point particles initially concentrated in a small region in $d$ dimensions. Particles undergo overdamped motion caused by pairwise interactions through the long-ranged repulsive $r^{-s}$ potential; each particle is also subject to Brownian noise. When $s<d$, the expansion is governed by non-local hydrodynamic equations. In the one-dimensional case, we deduce self-similar solutions for all $s\in (-2,1)$. The expansion of Coulomb gases remains well-defined in the infinite-particle limit: The density is spatially uniform and inversely proportional to time independent of the spatial dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14875 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Expansion into the vacuum of stochastic gases with long-range interactions Krapivsky, P. L. Mallick, Kirone Statistical Mechanics Mathematical Physics We study the evolution of a system of many point particles initially concentrated in a small region in $d$ dimensions. Particles undergo overdamped motion caused by pairwise interactions through the long-ranged repulsive $r^{-s}$ potential; each particle is also subject to Brownian noise. When $s<d$, the expansion is governed by non-local hydrodynamic equations. In the one-dimensional case, we deduce self-similar solutions for all $s\in (-2,1)$. The expansion of Coulomb gases remains well-defined in the infinite-particle limit: The density is spatially uniform and inversely proportional to time independent of the spatial dimension. |
| title | Expansion into the vacuum of stochastic gases with long-range interactions |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2412.14875 |