Mathematicians E (Princeton U.) and Lu (New York U.) study the solution to the Kohn-Sham equation in the density functional theory of the quantum many-body problem in the context of the electronic structure of the smoothly deformed macroscopic crystals. With an eye on the classical Cauchy-Born rule for crystal lattices, they establish an analog for the electronic structure of the deformed crystal under specific conditions. These conditions are the band structure of the undeformed crystal has a gap, so that the crystal is an insulator; the charge density waves are stable; and the macroscopic dielectric tensor is positive definite. They rigorously derive the equation governing the piezoelectric effect of a material, and along the way establish a number of fundamental properties of the Kohn-Sham map. They do not provide an index. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com)
