A mathematical formulation of the random phase approximation for crystals
Abstract
This works extends the recent study on the dielectric permittivity of crystals within the Hartree model [E. Cances and M. Lewin, Arch. Rational Mech. Anal., 197 (2010) 139--177] to the time-dependent setting. In particular, we prove the existence and uniqueness of the nonlinear Hartree dynamics (also called the random phase approximation in the physics literature), in a suitable functional space allowing to describe a local defect embedded in a perfect crystal. We also give a rigorous mathematical definition of the microscopic frequency-dependent polarization matrix, and derive the macroscopic Maxwell-Gauss equation for insulating and semiconducting crystals, from a first order approximation of the nonlinear Hartree model, by means of homogenization arguments.
Cite
@article{arxiv.1109.2416,
title = {A mathematical formulation of the random phase approximation for crystals},
author = {Eric Cances and Gabriel Stoltz},
journal= {arXiv preprint arXiv:1109.2416},
year = {2015}
}