| The Elastic Continuum Limit of the Tight Binding Model |
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| 引用本文： | Weinan E~* Jianfeng LU~(**) *Department of Mathematics and Program in Applied and Computational Mathematics,Princeton University,Princeton,NJ 08544,USA. **Program in Applied and Computational Mathematics,Princeton University,Princeton,NJ 08544,USA.. The Elastic Continuum Limit of the Tight Binding Model[J]. 数学年刊B辑(英文版), 2007, 28(6): 665-676. DOI: 10.1007/s11401-006-0447-2 |
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| 作者姓名： | Weinan E~* Jianfeng LU~(**) *Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA. **Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA. |
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| 作者单位： | Weinan E（Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA） ;Jianfeng LU（Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA） ; |
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| 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.
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| 关 键 词： | 闭联集 弹性理论 柯西级数 解题方法 |
| 收稿时间： | 2006-10-19 |
The Elastic Continuum Limit of the Tight Binding Model* |
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| Weinan E,Jianfeng Lu. The Elastic Continuum Limit of the Tight Binding Model*[J]. Chinese Annals of Mathematics,Series B, 2007, 28(6): 665-676. DOI: 10.1007/s11401-006-0447-2 |
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| Authors: | Weinan E Jianfeng Lu |
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| Affiliation: | 1. Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA
2. Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA |
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| Abstract: | 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. |
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| Keywords: | Continuum limit Elasticity theory Cauchy-Born rule Tight bindingmodel |
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