Minimum energy configurations of classical charges: Large N asymptotics

Understand

We study minimum energy configurations of $N$ particles in $\R^3$ of charge -1 (`electrons') in the potential of $M$ particles of charges $Z_\alpha>0$ (`atomic nuclei').

• In a suitable large-N limit, we determine the asymptotic electron distribution explicitly, showing in particular that the number of electrons surrounding each nucleus is asymptotic to the nuclear charge ("screening").
• The proof proceeds by establishing, via Gamma-convergence, a coarse-grained variational principle for the limit distribution, which can be solved explicitly.