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.
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.
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Mots-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
@article{CRMECA_2015__343_5-6_360_0, author = {Sergei A. Nazarov and Keijo Ruotsalainen and Pauliina Uusitalo}, title = {Asymptotics of the spectrum of the {Dirichlet} {Laplacian} on a thin carbon nano-structure}, journal = {Comptes Rendus. M\'ecanique}, pages = {360--364}, publisher = {Elsevier}, volume = {343}, number = {5-6}, year = {2015}, doi = {10.1016/j.crme.2015.03.001}, language = {en}, }
TY - JOUR AU - Sergei A. Nazarov AU - Keijo Ruotsalainen AU - Pauliina Uusitalo TI - Asymptotics of the spectrum of the Dirichlet Laplacian on a thin carbon nano-structure JO - Comptes Rendus. Mécanique PY - 2015 SP - 360 EP - 364 VL - 343 IS - 5-6 PB - Elsevier DO - 10.1016/j.crme.2015.03.001 LA - en ID - CRMECA_2015__343_5-6_360_0 ER -
%0 Journal Article %A Sergei A. Nazarov %A Keijo Ruotsalainen %A Pauliina Uusitalo %T Asymptotics of the spectrum of the Dirichlet Laplacian on a thin carbon nano-structure %J Comptes Rendus. Mécanique %D 2015 %P 360-364 %V 343 %N 5-6 %I Elsevier %R 10.1016/j.crme.2015.03.001 %G en %F CRMECA_2015__343_5-6_360_0
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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