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arXiv · 1109.2416

A mathematical formulation of the random phase approximation for crystals

Eric Cances·Gabriel Stoltz
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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.

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Eric Cances, Gabriel Stoltz. 2011-09-12. A mathematical formulation of the random phase approximation for crystals. https://doi.org/10.1016/j.anihpc.2012.05.004

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