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UID:3581@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20150127T110000
DTEND;TZID=Europe/Paris:20150127T120000
DTSTAMP:20150112T100000Z
URL:https://www.i2m.univ-amu.fr/events/classical-coulomb-gases-mean-field-
approximation-and-beyond/
SUMMARY:Classical Coulomb gases: mean-field approximation and beyond -
DESCRIPTION:Consider a system of N classical charged particles interacting
via Coulomb forces in space dimension d=2 or larger\, trapped in a confini
ng electrostatic potential. The 3D case is particularly relevant physicall
y\, and the 2D case is connected to several other problems: random matrice
s\, Fekete points\, Ginzburg-Landau theory\, quantum Hall states ...Assumi
ng that the strength of the interaction scales as the inverse of N (mean-f
ield regime)\, it is well-known that the leading order of the ground state
energy is given by a mean-field (continuum) theory. In this talk we are i
nterested in investigating the fluctuations around mean-field theory. We d
escribe these by the minimization of a "renormalized energy" functional th
at gives the energy per unit volume of infinitely many charged particles i
nteracting with each other and with a constant neutralizing background of
opposite charge (that is\, a Jellium).Results in two directions follow:- q
uantitative estimates on the precision of mean-field theory- identificatio
n of the next to leading order correction in the small temperature limitJo
int work with Sylvia Serfaty[http://www.ann.jussieu.fr/~rougerie/]
CATEGORIES:Séminaire Analyse Appliquée (AA)
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