Minimum energy configurations of classical charges: Large N asymptotics
Abstract
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 largeN 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 Gammaconvergence, a coarsegrained variational principle for the limit distribution, which can be solved explicitly.
 Publication:

arXiv eprints
 Pub Date:
 July 2009
 arXiv:
 arXiv:0907.5097
 Bibcode:
 2009arXiv0907.5097C
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 49XX;
 70C20;
 81V55
 EPrint:
 To appear in Applied Mathematics Research Express