Chinese Annals of Mathematics, Series B

, Volume 28, Issue 6, pp 665–676

The Elastic Continuum Limit of the Tight Binding Model*

ORIGINAL ARTICLES

DOI: 10.1007/s11401-006-0447-2

Cite this article as:
E, W. & Lu, J. Chin. Ann. Math. Ser. B (2007) 28: 665. doi:10.1007/s11401-006-0447-2

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.

Keywords

Continuum limit Elasticity theory Cauchy-Born rule Tight binding model 

2000 MR Subject Classification

74B20 35Q72 

Copyright information

© The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.Department of Mathematics and Program in Applied and Computational MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Program in Applied and Computational MathematicsPrinceton UniversityPrincetonUSA

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