Publications [#243749] of Jianfeng Lu

Papers Published

1. E, W; Lu, J, The Kohn-Sham equation for deformed crystals, Memoirs of the American Mathematical Society, vol. 221 no. 1040 (2012), pp. 1-1, American Mathematical Society (AMS), ISSN 0065-9266 [doi]
   (last updated on 2026/01/14)

   Abstract:
   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, we also establish a number of fundamental properties of the Kohn-Sham map. © 2012 by the American Mathematical Society. All rights reserved.