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 they give rise to a variety of questions pertaining to analysis, Partial Differential Equations and probability. We will first review these motivations, then present the "mean-field" derivation of effective models and equations describing the system at the macroscopic scale. We then explain how to analyze the next order behavior, giving information on the configurations at the microscopic level and connecting with crystallization questions, and finish with the description of the effect of temperature
https://eta.impa.br/dl/PL021.pdf
https://arxiv.org/abs/1712.04095
具有库仑相互作用的多体系统出现在：凝聚态物理和流体中的涡旋，逼近论，统计力学和量子力学，等离子体，随机矩阵论和复几何等领域。本文研究了平均场极限和宏观行为，并进一步研究了它们的微观行为。
相关附件
2-PL021 Serfaty.pdf
