Classical Coulomb gases: mean-field approximation and beyond

Date(s) : 27/01/2015   iCal
11 h 00 min - 12 h 00 min

Consider a system of N classical charged particles interacting via Coulomb forces in space dimension d=2 or larger, trapped in a confining electrostatic potential. The 3D case is particularly relevant physically, and the 2D case is connected to several other problems: random matrices, Fekete points, Ginzburg-Landau theory, quantum Hall states …

Assuming 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 state 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 of opposite charge (that is, a Jellium).

Results in two directions follow:
– quantitative estimates on the precision of mean-field theory
– identification of the next to leading order correction in the small temperature limit

Joint work with Sylvia Serfaty



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