Systems of points with Coulomb interactions – Sylvia Serfaty – ICM2018 скачать в хорошем качестве

Systems of points with Coulomb interactions – Sylvia Serfaty – ICM2018

Plenary Lecture 2 Systems of points with Coulomb interactions Sylvia Serfaty 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. ICM 2018 – International Congress of Mathematicians © www.icm2018.org     Os direitos sobre todo o material deste canal pertencem ao Instituto de Matemática Pura e Aplicada, sendo vedada a utilização total ou parcial do conteúdo sem autorização prévia e por escrito do referido titular, salvo nas hipóteses previstas na legislação vigente. The rights over all the material in this channel belong to the Instituto de Matemática Pura e Aplicada, and it is forbidden to use all or part of it without prior written authorization from the above mentioned holder, except in the cases prescribed in the current legislation.