Electronic structure of smoothly deformed crystals: Cauchy-Born rule for the nonlinear tight-binding model

E. Weinan; Jianfeng Lu

doi:10.1002/cpa.20330

Electronic structure of smoothly deformed crystals: Cauchy-Born rule for the nonlinear tight-binding model

E. Weinan, Jianfeng Lu

Mathematics

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

21 Scopus citations

Abstract

The electronic structure of a smoothly deformed crystal is analyzed using a minimalist model in quantum many-body theory, the nonlinear tight-binding model. An extension of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure under sharp stability conditions. A nonlinear elasticity model is rigorously derived. The onset of instability is briefly examined.

Original language	English (US)
Pages (from-to)	1432-1468
Number of pages	37
Journal	Communications on Pure and Applied Mathematics
Volume	63
Issue number	11
DOIs	https://doi.org/10.1002/cpa.20330
State	Published - Nov 2010

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1002/cpa.20330

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title = "Electronic structure of smoothly deformed crystals: Cauchy-Born rule for the nonlinear tight-binding model",

abstract = "The electronic structure of a smoothly deformed crystal is analyzed using a minimalist model in quantum many-body theory, the nonlinear tight-binding model. An extension of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure under sharp stability conditions. A nonlinear elasticity model is rigorously derived. The onset of instability is briefly examined.",

author = "E. Weinan and Jianfeng Lu",

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AU - Lu, Jianfeng

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AB - The electronic structure of a smoothly deformed crystal is analyzed using a minimalist model in quantum many-body theory, the nonlinear tight-binding model. An extension of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure under sharp stability conditions. A nonlinear elasticity model is rigorously derived. The onset of instability is briefly examined.

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Electronic structure of smoothly deformed crystals: Cauchy-Born rule for the nonlinear tight-binding model

Abstract

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