Eigenvalue and Resonance Asymptotics in perturbed periodically twisted tubes: Twisting versus Bending
| Autor: | Pablo A. Miranda, Vincent Bruneau, Nicolas Popoff, Daniel Parra |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Departamento de Matemática y Ciencia de la Computación [Santiago de Chile] (DMCC), Probabilités, statistique, physique mathématique (PSPM), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Nuclear and High Energy Physics
Essential spectrum FOS: Physical sciences 01 natural sciences Mathematics - Spectral Theory [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] 0103 physical sciences FOS: Mathematics Waveguide (acoustics) 0101 mathematics Spectral Theory (math.SP) Eigenvalues and eigenvectors ComputingMilieux_MISCELLANEOUS Mathematical Physics Resolvent Coupling constant Physics 010102 general mathematics Mathematical analysis Spectrum (functional analysis) Resonance Statistical and Nonlinear Physics Mathematical Physics (math-ph) 010307 mathematical physics Asymptotic expansion [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] |
| Zdroj: | Annales Henri Poincaré Annales Henri Poincaré, Springer Verlag, 2020, 21 (2), pp.377-403. ⟨10.1007/s00023-019-00865-5⟩ |
| ISSN: | 1424-0637 1424-0661 |
| DOI: | 10.1007/s00023-019-00865-5⟩ |
| Popis: | We consider a three-dimensional waveguide that is a small deformation of a periodically twisted tube (including in particular the case of a straight tube). The deformation is given by a bending and an additional twisting of the tube, both parametrized by a coupling constant $$\delta $$. In this deformed waveguide, we consider the Dirichlet Laplacian. We expand its resolvent near the bottom of its essential spectrum, and we show the existence of exactly one resonance, in the asymptotic regime of $$\delta $$ small. We are able to perform the asymptotic expansion of the resonance in $$\delta $$, which in particular permits us to give a quantitative geometric criterion for the existence of a discrete eigenvalue below the essential spectrum. In the case of perturbations of straight tubes, we are able to show the existence of resonances not only near the bottom of the essential spectrum but near each threshold in the spectrum, showing in particular what are the spectral effects of the bending for higher energies. We also obtain the asymptotic behavior of the resonances in this situation, which is generically different from the first case. |
| Databáze: | OpenAIRE |
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