The Elastic Continuum Limit of the Tight Binding Model
The Elastic Continuum Limit of the Tight Binding Model作者机构: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
出 版 物:《Chinese Annals of Mathematics,Series B》 (数学年刊(B辑英文版))
年 卷 期:2007年第28卷第6期
页 面:665-676页
核心收录:
学科分类:07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金:Project supported by the Natural Science Foundation(No. DMS 04-07866) the "Research Team on Complex Systems" of Chinese Academy of Sciences
主 题:Continuum limit Elasticity theory Cauchy-Born rule Tight binding model
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.