The Kohn-Sham equation for deformed crystals

E. Weinan, Jianfeng Lu

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


The solution to the Kohn-Sham equation in the density functional theory of the quantum many-body problem is studied in the context of the electronic structure of smoothly deformed macroscopic crystals. An analog of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure of the deformed crystal under the following physical conditions: (1) the band structure of the undeformed crystal has a gap, i.e. the crystal is an insulator, (2) the charge density waves are stable, and (3) the macroscopic dielectric tensor is positive definite. The effective equation governing the piezoelectric effect of a material is rigorously derived. Along the way, we also establish a number of fundamental properties of the Kohn-Sham map.

Original languageEnglish (US)
Pages (from-to)1-109
Number of pages109
JournalMemoirs of the American Mathematical Society
Issue number1040
StatePublished - Jan 2013

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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