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Gaps in the spectrum of the Neumann Laplacian generated by a system of periodically distributed traps |
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| Authors: | Andrii Khrabustovskyi Evgeni Khruslov |
| Affiliation: | 1. Department of Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany Correspondence to: Andrii Khrabustovskyi, Department of Mathematics, Karlsruhe Institute of Technology, Kaiserstrasse 89-93, Karlsruhe 76133, Germany. E-mail: andrii.khrabustovskyi@kit.edu;2. Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Lenin Ave., Kharkov 61103, Ukraine |
| Abstract: | The article deals with a convergence of the spectrum of the Neumann Laplacian in a periodic unbounded domain Ωϵ depending on a small parameter ϵ > 0. The domain has the form  , where Sϵ is an  -periodic family of trap-like screens. We prove that, for an arbitrarily large L, the spectrum has precisely one gap in [0,L] when ϵ is small enough; moreover, when ϵ → 0, this gap converges to some interval whose edges can be controlled by a suitable choice of geometry of the screens. An application to the theory of 2D photonic crystals is discussed. Copyright © 2014 John Wiley & Sons, Ltd. |
| Keywords: | periodic domain Neumann Laplacian spectrum gaps |