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portada Descargar ficha PDF Título: Kohn-Sham Equation For Deformed Crystals
Autor: Weinan E; Jianfeng Lu Precio: $1007.86
Editorial: American Mathematical Society Año: 2013
Tema: Edición: 1ª
Sinopsis ISBN: 9780821875605
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.

Table of Contents

¦Introduction
¦Perfect crystal
¦Stability condition
¦Homogeneously deformed crystal
¦Deformed crystal and the extended Cauchy-Born rule
¦The linearized Kohn-Sham operator
¦Proof of the results for the homogeneously deformed crystal
¦Exponential decay of the resolvent
¦Asymptotic analysis of the Kohn-Sham equation
¦Higher order approximate solution to the Kohn-Sham equation
¦Proofs of Lemmas 5.3 and 5.4
¦Appendix A. Proofs of Lemmas 9.3 and 9.9
¦Bibliography
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