The Kohn-Sham Equation for Deformed Crystals
Author： Weinan E;Jianfeng Lu
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9780821894668
P-ISBN(Paperback): 9780821875605
P-ISBN(Hardback): 9780821875605
Subject： O733 Mechanical properties of crystals
Keyword： Differential Equations
Language： ENG
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The Kohn-Sham Equation for Deformed Crystals
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.