The Kohn-Sham Equation for Deformed Crystals

(Memoirs of the American Mathematical Society)

5bc04c53eecab.jpg Author Weinan E.
Isbn 9780821875605
File size 780.59KB
Year 2013
Pages 96
Language English
File format PDF
Category Mathematics

Book Description:

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



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