Comptes Rendus
no. 5-6
Asymptotics of the spectrum of the Dirichlet Laplacian on a thin carbon nano-structure
[Analyse asymptotique du spectre de l'opérateur laplacien de Dirichlet dans une fine nano-structure de carbone]
Sergei A. Nazarov1, 2 ; Keijo Ruotsalainen3 ; Pauliina Uusitalo3 
1 Saint-Petersburg State University, Universitetsky pr., 28, Peterhof, St. Petersburg, 198504, Russia
2 Saint-Petersburg State Polytechnical University, Polytechnicheskaya ul., 29, St. Petersburg, 195251, Russia
3 University of Oulu, Mathematics Division, P.O. Box 4500, 90014, Oulu, Finland
Comptes Rendus. Mécanique, Volume 343 (2015) no. 5-6, pp. 360-364.

Pour la structure en nid d'abeille du guide d'ondes quantique, on réalise un passage à la limite lorsque l'épaisseur relative h des liaisons tend vers zéro, et on décrit le comportement asymptotique du spectre de l'opérateur laplacien de Dirichlet.

For the honeycomb lattice of quantum waveguides, the limit passage is performed when the relative thickness h of ligaments tends to zero and the asymptotic structure of the spectrum of the Dirichlet Laplacian is described.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2015.03.001
Keywords: Spectrum, Dirichlet problem, Asymptotics, Quantum waveguide, Trapped modes and bounded solutions
Mot clés : Spectre, Opérateur laplacien de Dirichlet, Analyse asymptotique, Guides d'ondes quantiques, Modes piégés et solutions bornées
Sergei A. Nazarov 1, 2 ; Keijo Ruotsalainen 3 ; Pauliina Uusitalo 3

1 Saint-Petersburg State University, Universitetsky pr., 28, Peterhof, St. Petersburg, 198504, Russia
2 Saint-Petersburg State Polytechnical University, Polytechnicheskaya ul., 29, St. Petersburg, 195251, Russia
3 University of Oulu, Mathematics Division, P.O. Box 4500, 90014, Oulu, Finland 
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Sergei A. Nazarov; Keijo Ruotsalainen; Pauliina Uusitalo. Asymptotics of the spectrum of the Dirichlet Laplacian on a thin carbon nano-structure. Comptes Rendus. Mécanique, Volume 343 (2015) no. 5-6, pp. 360-364. doi : 10.1016/j.crme.2015.03.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.03.001/

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