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Section
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Mathematics
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Title
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Scattering and quasilevels in the SSH model
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Author(-s)
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Tinyukova T.S.a
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Affiliations
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Udmurt State Universitya
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Abstract
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Topological insulator is a special type of material that represents an insulator in the interior (“in bulk”) and conducts electricity on the surface. The simplest topological insulator is a finite chain of atoms in polyacetylene. In the last decade topological insulators are actively studied in the physics literature. A great interest to topological insulators (and also to topologically similar superconducting systems) is due to the presence of a link between “volume” and “boundary”. In this article, we have studied the discrete model SSH (Su-Schrieffer-Heeger) for polyacetylene. This model describes an electron in a one-dimensional chain of atoms with two alternating amplitudes of the transition to a neighboring atom. We have found the spectrum and resolution of this operator. The quasilevels (eigenvalues and resonances) in the case of a small potential have been investigated. In addition, we obtained a solution of the Lippmann-Schwinger equation and asymptotic formulas for the probability of transmission and reflection in case of small perturbation.
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Keywords
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resolution, spectrum, eigenvalue, resonance, Lippmann-Schwinger equation, probability of reflection
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UDC
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517.958, 530.145.6
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MSC
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81Q10, 81Q15
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DOI
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10.20537/vm170209
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Received
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1 February 2017
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Language
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Russian
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Citation
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Tinyukova T.S. Scattering and quasilevels in the SSH model, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 2, pp. 257-266.
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References
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