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| HAL : hal-00652901, version 2 |
| arXiv : 1112.4263 |
| Fiche détaillée |  Récupérer au format |
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| ESAIM: Proceedings (2012) SMAI 2011, To appear |
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| Versions disponibles : | v1 (19-12-2011) | v2 (22-12-2011) |
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| Quantum waveguides with corners |
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| Monique Dauge 1Yvon Lafranche 1 |
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| (2012) |
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| The simplest modeling of planar quantum waveguides is the Dirichlet eigenproblem for the Laplace operator in unbounded open sets which are uniformly thin in one direction. Here we consider V-shaped guides. Their spectral properties depend essentially on a sole parameter, the opening of the V. The free energy band is a semi-infinite interval bounded from below. As soon as the V is not flat, there are bound states below the free energy band. There are a finite number of them, depending on the opening. This number tends to infinity as the opening tends to 0 (sharply bent V). In this situation, the eigenfunctions concentrate and become self-similar. In contrast, when the opening gets large (almost flat V), the eigenfunctions spread and enjoy a different self-similar structure. We explain all these facts and illustrate them by numerical simulations. |
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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université Rennes II |
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| Analyse numérique, Equations aux dérivées partielles |
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| Domaine | : | Mathématiques/Analyse numérique |
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| hal-00652901, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00652901 | |
| oai:hal.archives-ouvertes.fr:hal-00652901 | |
| Contributeur : Monique Dauge | |
| Soumis le : Jeudi 22 Décembre 2011, 14:15:30 | |
| Dernière modification le : Mercredi 4 Janvier 2012, 11:47:06 | |
