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| HAL: hal-00622929, version 1 |
| arXiv: 1109.2416 |
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| A mathematical formulation of the random phase approximation for crystals |
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| Eric Cances 1, 2Gabriel Stoltz 1, 2 |
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| (2011-09-12) |
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| 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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| 1: | Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) |
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Ecole des Ponts ParisTech |
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| 2: | MICMAC (INRIA Paris - Rocquencourt) |
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Ecole des Ponts ParisTech – INRIA |
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| Subject | : | Physics/Mathematical Physics Mathematics/Mathematical Physics |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1109.2416 |
| hal-00622929, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00622929 | |
| oai:hal.archives-ouvertes.fr:hal-00622929 | |
| From: Gabriel Stoltz | |
| Submitted on: Tuesday, 13 September 2011 09:59:23 | |
| Updated on: Tuesday, 13 September 2011 09:59:23 | |
