库仑作用点系
Systems of Points with Coulomb Interactions
摘要：
在凝聚态物理、经典力学和量子力学、统计力学、随机矩阵甚至近似理论的各种背景下，出现了大量具有库仑相互作用的点，并产生了与变分法、偏微分方程和概率有关的各种问题。我们将审查这些以及“平均场极限”的结果，允许导出有效的模型和方程描述系统在宏观尺度。然后，我们解释如何分析下一个订单超出平均场限制，在微观层面上的系统提供信息。在统计力学的背景下，这允许例如观察温度的影响并与结晶问题联系起来。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
