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| HAL: hal-00527022, version 1 |
| arXiv: 1010.3494 |
| DOI: 10.1007/978-3-642-21943-6 |
| Detailed view |  Export this paper |
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| Numerical Analysis of Multiscale Computations. Proceedings of a Winter Workshop at the Banff International Research Station 2009, Björn Engquist, Olof Runborg and Yen-Hsi R. Tsai (Ed.) (2011) 87--125 |
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| The Microscopic Origin of the Macroscopic Dielectric Permittivity of Crystals: A Mathematical Viewpoint |
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| Eric Cancès 1, 2Mathieu Lewin 3 |
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| (2011) |
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| The purpose of this paper is to provide a mathematical analysis of the Adler-Wiser formula relating the macroscopic relative permittivity tensor to the microscopic structure of the crystal at the atomic level. The technical level of the presentation is kept at its minimum to emphasize the mathematical structure of the results. We also briefly review some models describing the electronic structure of finite systems, focusing on density operator based formulations, as well as the Hartree model for perfect crystals or crystals with a defect. |
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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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| 3: | Laboratoire d'Analyse, Géométrie et Modélisation (AGM) |
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CNRS : UMR8088 – Université de Cergy Pontoise |
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| Subject | : | Physics/Mathematical Physics Mathematics/Mathematical Physics Physics/Condensed Matter/Materials Science Mathematics/Analysis of PDEs |
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| hal-00527022, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00527022 | |
| oai:hal.archives-ouvertes.fr:hal-00527022 | |
| From: Mathieu Lewin | |
| Submitted on: Sunday, 17 October 2010 22:19:01 | |
| Updated on: Tuesday, 10 July 2012 15:50:33 | |
