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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 163, Pages 3–14
(Mi into447)
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This article is cited in 1 scientific paper (total in 1 paper)
On occurrence of resonances from multiple eigenvalues of the Schrödinger operator in a cylinder with scattering perturbations
D. I. Borisovabc, A. M. Golovinad a Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
b Bashkir State Pedagogical University, Ufa
c University of Hradec Králové
d Bauman Moscow State Technical University
Abstract:
In this paper, the Schrödinger operator with a localized potential in a multidimensional cylinder is considered. The boundary of the cylinder is split into three parts, two of which are “sleeves” going to infinity, and the third (central) part is located between them. On the sleeves and the central part, respectively, the Neumann and Dirichlet boundary conditions are posed. We examine the situation where the distance between the sleeves increases. We assume that the same Schrödinger operator in the same cylinder endowed with the Dirichlet condition on the whole boundary has an isolated double eigenvalue. We show that for a sufficiently large distance between the sleeves, this double eigenvalue splits into a pair of resonances of the original operator. For these resonances, we explicitly obtain the first terms of their asymptotic expansions and describe the behavior of the imaginary part of the resonances.
Keywords:
Schrödinger operator, perturbation of continuous spectrum, resonance, scattering perturbation.
Citation:
D. I. Borisov, A. M. Golovina, “On occurrence of resonances from multiple eigenvalues of the Schrödinger operator in a cylinder with scattering perturbations”, Differential Equations, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 163, VINITI, Moscow, 2019, 3–14
Linking options:
https://www.mathnet.ru/eng/into447 https://www.mathnet.ru/eng/into/v163/p3
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Abstract page: | 150 | Full-text PDF : | 63 | References: | 15 | First page: | 1 |
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