The Kohn-Sham equation for deformed crystals

The Kohn-Sham equation for deformed crystals

Author
Weinan E., Jianfeng Lu
Publisher
Amer Mathematical Society
Language
English
Year
2013
Page
109
ISBN
0821875604,978-0-8218-7560-5
File Type
pdf
File Size
780.6 KiB

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 (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, the authors also establish a number of fundamental properties of the Kohn-Sham map.

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