Minimum energy configurations of classical charges: Large N asymptotics
Classical Analysis and ODEs
2009-07-30 v1
Abstract
We study minimum energy configurations of particles in of charge -1 (`electrons') in the potential of particles of charges (`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