The Elastic Continuum Limit of the Tight Binding Model

被引：0

作者：

Weinan E~* Jianfeng LU~(**) *Department of Mathematics and Program in Applied and Computational Mathematics

机构：

来源：

ChineseAnnalsofMathematics | 2007年 / 06期

关键词：

Continuum limit; Elasticity theory; Cauchy-Born rule; Tight binding model;

D O I：

暂无

中图分类号：

O481 [固体理论]; O175 [微分方程、积分方程];

学科分类号：

070104 ; 070205 ; 0805 ; 080502 ; 0809 ;

摘要：

The authors consider the simplest quantum mechanics model of solids,the tight binding model,and prove that in the continuum limit,the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule.The technique in this paper is based mainly on spectral perturbation theory for large matrices.

引用

页码：665 / 676

页数：12

共 13 条

[1] Cauchy–Born Rule and the Stability of Crystalline Solids: Static Problems[J] . Weinan E,Pingbing Ming. &nbspArchive for Rational Mechanics and Analysis . 2007 (2)
[2] From molecular models to continuum mechanics
Blanc, X
Le Bris, C
Lions, PL
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 164 (04) : 341 - 381
[3] Solid State Physics. Ashcroft,N,and Mermin,N. . 1976
[4] From molecular models to continuum mechanics. Blanc,X,Le Bris,C,and Lions,P.L. Archive for Rational Mechanics and Analysis . 2002
[5] DynamicaI Theory of CrystaI Lattices. Born,M,and Huang,K. . 1954
[6] L.Mathematical Theory of Thermodynamic Limits: Thomas-Fermi Type Models. Catto,I,Le Bris,C,and Lions,P. . 1998
[7] On the thermodynamic limit for Hartree-Fock type models. Catto,I,Le Bris,C,and Lions,P.L. Ann. Inst.Henri Poincaré . 2001
[8] On some periodic Hartree-type models for crystals. Catto,I,Le Bris,C,and Lions,P.L. Ann.Inst. Henri Poincaré . 2002
[9] The variation of the spectrum of a normal matrix. Hoffman,A. J. and Wielandt,H W. Duke Mathematical Journal . 1953
[10] Cauchy-Born rule and stability of crystalline solids: static problems. E,W,and Ming,P. Archive for Rational Mechanics and Analysis . 2007

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