The Kohn-Sham Equation for Deformed Crystals (Memoirs of the American Mathematical Society)
The Kohn-Sham Equation for Deformed Crystals (Memoirs of the American Mathematical Society) by Weinan E.
English | 2013 | ISBN: 0821875604 | 96 Pages | PDF | 780.59 KB
English | 2013 | ISBN: 0821875604 | 96 Pages | PDF | 780.59 KB
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.