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The Elastic Continuum Limit of the Tight Binding Model*

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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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Authors and Affiliations

  1. Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Weinan E

  2. Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Jianfeng Lu

Authors
  1. Weinan E
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  2. Jianfeng Lu
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Corresponding author

Correspondence to Weinan E.

Additional information

* Project supported by the Natural Science Foundation (No. DMS 04-07866) and the "Research Team on Complex Systems" of Chinese Academy of Sciences.

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E, W., Lu, J. The Elastic Continuum Limit of the Tight Binding Model*. Chin. Ann. Math. Ser. B 28, 665–676 (2007). https://doi.org/10.1007/s11401-006-0447-2

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  • DOI: https://doi.org/10.1007/s11401-006-0447-2

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