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UID:561@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20150127T110000
DTEND;TZID=Europe/Paris:20150127T120000
DTSTAMP:20150112T100000Z
URL:https://www.i2m.univ-amu.fr/evenements/classical-coulomb-gases-mean-fi
 eld-approximation-and-beyond/
SUMMARY: (...): Classical Coulomb gases: mean-field approximation and beyon
 d
DESCRIPTION:: Consider a system of N classical charged particles interactin
 g via Coulomb forces in space dimension d=2 or larger\, trapped in a confi
 ning electrostatic potential. The 3D case is particularly relevant physica
 lly\, and the 2D case is connected to several other problems: random matri
 ces\, Fekete points\, Ginzburg-Landau theory\, quantum Hall states ...Assu
 ming that the strength of the interaction scales as the inverse of N (mean
 -field regime)\, it is well-known that the leading order of the ground sta
 te energy is given by a mean-field (continuum) theory. In this talk we are
  interested in investigating the fluctuations around mean-field theory. We
  describe these by the minimization of a "renormalized energy" functional 
 that gives the energy per unit volume of infinitely many charged particles
  interacting with each other and with a constant neutralizing background o
 f opposite charge (that is\, a Jellium).Results in two directions follow:-
  quantitative estimates on the precision of mean-field theory- identificat
 ion of the next to leading order correction in the small temperature limit
 Joint work with Sylvia Serfaty[http://www.ann.jussieu.fr/~rougerie/]
CATEGORIES:Séminaire,Analyse Appliquée
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