Quantum waveguides with corners

Abstract : 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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Article dans une revue
ESAIM: Proceedings, EDP Sciences, 2012, 35, pp.14-45. 〈10.1051/proc/201235002〉
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https://hal.archives-ouvertes.fr/hal-00652901
Contributeur : Monique Dauge <>
Soumis le : jeudi 22 décembre 2011 - 14:15:30
Dernière modification le : vendredi 16 novembre 2018 - 01:25:17
Document(s) archivé(s) le : vendredi 23 mars 2012 - 02:31:13

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Monique Dauge, Yvon Lafranche, Nicolas Raymond. Quantum waveguides with corners. ESAIM: Proceedings, EDP Sciences, 2012, 35, pp.14-45. 〈10.1051/proc/201235002〉. 〈hal-00652901v2〉

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