Electronic structure of smoothly deformed crystals: Cauchy-Born rule for the nonlinear tight-binding model

E. Weinan, Jianfeng Lu

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

The electronic structure of a smoothly deformed crystal is analyzed using a minimalist model in quantum many-body theory, the nonlinear tight-binding model. An extension of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure under sharp stability conditions. A nonlinear elasticity model is rigorously derived. The onset of instability is briefly examined.

Original languageEnglish (US)
Pages (from-to)1432-1468
Number of pages37
JournalCommunications on Pure and Applied Mathematics
Volume63
Issue number11
DOIs
StatePublished - Nov 1 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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