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| HAL: hal-00652901, version 2 |
| arXiv: 1112.4263 |
| DOI: 10.1051/proc/201235002 |
| Detailed view |  Export this paper |
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| ESAIM: Proceedings 35 (2012) 14-45 |
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| Available versions: | v1 (2011-12-19) | v2 (2011-12-22) |
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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 – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Analyse numérique Equations aux dérivées partielles |
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| Subject | : | Mathematics/Numerical Analysis |
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| hal-00652901, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00652901 | |
| oai:hal.archives-ouvertes.fr:hal-00652901 | |
| From: Monique Dauge | |
| Submitted on: Thursday, 22 December 2011 14:15:30 | |
| Updated on: Thursday, 6 September 2012 15:35:42 | |
