English

Minimum energy configurations of classical charges: Large N asymptotics

Classical Analysis and ODEs 2009-07-30 v1

Abstract

We study minimum energy configurations of NN particles in R3\R^3 of charge -1 (`electrons') in the potential of MM particles of charges Zα>0Z_\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.

Keywords

Cite

@article{arxiv.0907.5097,
  title  = {Minimum energy configurations of classical charges: Large N asymptotics},
  author = {Stephane Capet and Gero Friesecke},
  journal= {arXiv preprint arXiv:0907.5097},
  year   = {2009}
}

Comments

To appear in Applied Mathematics Research Express