Minimum energy configurations of classical charges in the potential of an atomic nucleus: Large N asymptotics

This problem offers a simple setting in which some aspects of the notorious many-body Coulomb interaction can be understood using relatively `easy' analysis. These aspects -- such as "screening" -- are of fundamental importance in ion physics and quantum chemistry, but previous mathematical analysis (which I will briefly review) has been somewhat heavy going.

The key observation is that the problem has an interesting and explicit Gamma limit as N tends to infinity, which may be viewed as a classical analogue of Thomas-Fermi theory. From this one infers, among other things, an angular equidistribution law, a radial condensation law, and asymptotic neutrality of the crossover point from attainment to nonattainment (recovering a result by Lieb, Loss, Sigal, and Solovej).

The methods are hoped to be applicable to much more general many-body Coulomb systems, including quantum mechanical ones.

Joint work with Stephane Capet (Munich/Warwick).