Expansion into the vacuum of stochastic gases with long-range interactions

P. L. Krapivsky; Kirone Mallick

doi:10.1103/physreve.111.064109

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arXiv · 2412.14875

Expansion into the vacuum of stochastic gases with long-range interactions

P. L. Krapivsky·Kirone Mallick

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Abstract

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.

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P. L. Krapivsky, Kirone Mallick. 2024-12-19. Expansion into the vacuum of stochastic gases with long-range interactions. https://doi.org/10.1103/physreve.111.064109

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