Systems of points with Coulomb interactions

Sylvia Serfaty

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationInvited Lectures
EditorsBoyan Sirakov, Paulo Ney de Souza, Marcelo Viana
PublisherWorld Scientific Publishing Co. Pte Ltd
Pages935-978
Number of pages44
ISBN (Electronic)9789813272903
StatePublished - 2018
Event2018 International Congress of Mathematicians, ICM 2018 - Rio de Janeiro, Brazil
Duration: Aug 1 2018Aug 9 2018

Publication series

NameProceedings of the International Congress of Mathematicians, ICM 2018
Volume1

Conference

Conference2018 International Congress of Mathematicians, ICM 2018
CountryBrazil
CityRio de Janeiro
Period8/1/188/9/18

Keywords

  • Coulomb gases
  • Crystallization
  • Gaussian Free Field
  • Jellium
  • Large deviations
  • Log gases
  • Mean field limits
  • Point processes

ASJC Scopus subject areas

  • Mathematics(all)

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