Existence of minimizers for Kohn-Sham within the local spin density approximation

David Gontier

doi:10.1088/0951-7715/28/1/57

Existence of minimizers for Kohn-Sham within the local spin density approximation

David Gontier

Research output: Contribution to journal › Article › peer-review

Abstract

The purpose of this article is to extend the work by Anantharaman and Cancès (2009 Ann. Inst. Henri Poincaré (C) 26 2425-55) and prove the existence of minimizers for the spin-polarized Kohn-Sham model in the presence of a magnetic field within the local spin density approximation. We show that for any magnetic field that vanishes at infinity, the existence of minimizers is ensured for neutral or positively charged systems. The proof relies on classical concentration-compactness techniques.

Original language	English
Article number	57
Pages (from-to)	57-76
Number of pages	20
Journal	Nonlinearity
Volume	28
Issue number	1
DOIs	https://doi.org/10.1088/0951-7715/28/1/57
Publication status	Published - 1 Jan 2015

Keywords

Concentration-compactness
Kohn-Sham
Spin density functional theory

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10.1088/0951-7715/28/1/57

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abstract = "The purpose of this article is to extend the work by Anantharaman and Canc{\`e}s (2009 Ann. Inst. Henri Poincar{\'e} (C) 26 2425-55) and prove the existence of minimizers for the spin-polarized Kohn-Sham model in the presence of a magnetic field within the local spin density approximation. We show that for any magnetic field that vanishes at infinity, the existence of minimizers is ensured for neutral or positively charged systems. The proof relies on classical concentration-compactness techniques.",

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AB - The purpose of this article is to extend the work by Anantharaman and Cancès (2009 Ann. Inst. Henri Poincaré (C) 26 2425-55) and prove the existence of minimizers for the spin-polarized Kohn-Sham model in the presence of a magnetic field within the local spin density approximation. We show that for any magnetic field that vanishes at infinity, the existence of minimizers is ensured for neutral or positively charged systems. The proof relies on classical concentration-compactness techniques.

KW - Concentration-compactness

KW - Kohn-Sham

KW - Spin density functional theory

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Existence of minimizers for Kohn-Sham within the local spin density approximation

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Keywords

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