A mathematical formulation of the random phase approximation for crystals - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2011

A mathematical formulation of the random phase approximation for crystals

Résumé

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.

Dates et versions

hal-00622929 , version 1 (13-09-2011)

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Eric Cancès, Gabriel Stoltz. A mathematical formulation of the random phase approximation for crystals. 2011. ⟨hal-00622929⟩
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