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The Two-Particle Correlation Function for Systems with Long-Range Interactions

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Abstract

In this paper, we study the truncated two-particle correlation function in particle systems with long range interactions. For Coulombian and soft potentials, we define and give well-posedness results for the equilibrium correlations. In the Coulombian case, we prove the onset of the Debye screening length in the equilibrium correlations, for suitable velocity distributions. Additionally, we give precise estimates on the effective range of interaction between particles. In the case of soft potential interaction the equilibrium correlations and their fluxes in the space of velocities are shown to be linearly stable.

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Acknowledgements

The authors acknowledge support through the CRC 1060 The mathematics of emergent effects at the University of Bonn that is funded through the German Science Foundation (DFG).

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Authors and Affiliations

  1. Institute for Applied Mathematics, University of Bonn, Bonn, Germany

    Juan J. L. Velázquez & Raphael Winter

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  1. Juan J. L. Velázquez
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  2. Raphael Winter
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Correspondence to Raphael Winter.

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Velázquez, J.J.L., Winter, R. The Two-Particle Correlation Function for Systems with Long-Range Interactions. J Stat Phys 173, 1–41 (2018). https://doi.org/10.1007/s10955-018-2121-y

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