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Minimum energy configurations of classical charges : large N asymptotics
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Capet, S. and Friesecke, Gero (2009) Minimum energy configurations of classical charges : large N asymptotics. Applied Mathematics Research eXpress, Vol.2009 (No.1). pp. 47-73. doi:10.1093/amrx/abp002 ISSN 1687-1200.
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Official URL: http://dx.doi.org/10.1093/amrx/abp002
Abstract
We study the minimum energy configurations of N particles in of charge −1 (“electrons”) in the potential of M particles of charges Zα > 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.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Applied Mathematics Research eXpress | ||||
| Publisher: | Oxford University Press | ||||
| ISSN: | 1687-1200 | ||||
| Official Date: | 2009 | ||||
| Dates: |
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| Volume: | Vol.2009 | ||||
| Number: | No.1 | ||||
| Page Range: | pp. 47-73 | ||||
| DOI: | 10.1093/amrx/abp002 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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