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Conference on "Mathematical properties of large quantum systems"
Organizers: Maria J. Esteban (CNRS), Mathieu Lewin (CNRS), Robert Seiringer (McGill, Montréal) & Jan Philip Solovej (Copenhagen)


Sylvia Serfaty (Paris, France): "Higher dimensional Coulomb gases: ground states, thermal states, and renormalized energy"
Friday 21 June 2013, 15:20 - 16:05
Amphi Hermite


This is joint work with Nicolas Rougerie. We are interested in a classical Coulomb gas in a confining potential, in any dimension larger than 2.

We accomplish the program carried out by Sandier-Serfaty in dimension 2, but this time for arbitrary dimensions, and via a different method. The method relies on smearing out of charges and Onsager's lemma, and allows to define a new "renormalized energy", which we show governs the next order fluctuations in the distribution of particles beyond the mean-field limit. Results include a next order expansion of the ground state energy, a next order expansion of the free energy for nonzero temperature cases, and a crystallization conjecture.