Minimum energy configurations of classical charges: Large N asymptotics

Details Minimum energy configurations of classical charges: Large N asymptotics Minimum energy configurations of classical charges: Large N asymptotics

2009-07-29

arxiv.org/abs/0907.5097v1

Mathematics

Classical Analysis and ODEs

To appear in Applied Mathematics Research Express

Scientific paper

10.1093/amrx/abp002

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.

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