Stability and the continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model

E. Weinan; Jianfeng Lu

doi:10.1063/1.4755952

Stability and the continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model

E. Weinan, Jianfeng Lu

Mathematics

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Abstract

The continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model in an external magnetic field is studied. An extension of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure under sharp stability conditions on charge density and spin density waves. A Landau-Lifshitz type of micromagnetic energy functional is derived.

Original language	English (US)
Article number	115615
Journal	Journal of Mathematical Physics
Volume	53
Issue number	11
DOIs	https://doi.org/10.1063/1.4755952
State	Published - Nov 27 2012

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.4755952

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abstract = "The continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizs{\"a}cker model in an external magnetic field is studied. An extension of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure under sharp stability conditions on charge density and spin density waves. A Landau-Lifshitz type of micromagnetic energy functional is derived.",

author = "E. Weinan and Jianfeng Lu",

note = "Funding Information: The work of E is supported in part by the National Science Foundation (NSF) Grant Nos. DMS-0708026 and DMS-0914336, the ONR Grant No. N00014-01-1-0674, and the (U.S.) Department of Energy (DOE) Grant No. DE-FG02-03ER25587.",

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T1 - Stability and the continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model

AU - Weinan, E.

AU - Lu, Jianfeng

N1 - Funding Information: The work of E is supported in part by the National Science Foundation (NSF) Grant Nos. DMS-0708026 and DMS-0914336, the ONR Grant No. N00014-01-1-0674, and the (U.S.) Department of Energy (DOE) Grant No. DE-FG02-03ER25587.

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Y1 - 2012/11/27

N2 - The continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model in an external magnetic field is studied. An extension of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure under sharp stability conditions on charge density and spin density waves. A Landau-Lifshitz type of micromagnetic energy functional is derived.

AB - The continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model in an external magnetic field is studied. An extension of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure under sharp stability conditions on charge density and spin density waves. A Landau-Lifshitz type of micromagnetic energy functional is derived.

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Stability and the continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model

Abstract

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