Systems of Points with Coulomb Interactions
Abstract
Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and give rise to a variety of questions pertaining to calculus of variations, Partial Differential Equations and probability. We will review these as well as "the mean-field limit" results that allow to derive effective models and equations describing the system at the macroscopic scale. We then explain how to analyze the next order beyond the mean-field limit, giving information on the system at the microscopic level. In the setting of statistical mechanics, this allows for instance to observe the effect of the temperature and to connect with crystallization questions.
Cite
@article{arxiv.1712.04095,
title = {Systems of Points with Coulomb Interactions},
author = {Sylvia Serfaty},
journal= {arXiv preprint arXiv:1712.04095},
year = {2018}
}
Comments
30 pages, to appear as Proceedings of the ICM2018