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Edge states in ordinary differential equations for dislocations

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1908.01377.pdf (462.4Kb)
Date
2020-04
Dewey
Analyse
Sujet
Operator theory; Functional analysis; Hellmann Feynman theorem; Dirac equation; Hill equation; Quantum mechanical operators
Journal issue
Journal of Mathematical Physics
Volume
61
Number
4
Publication date
04-2020
Publisher
American Institute of Physics
DOI
http://dx.doi.org/10.1063/1.5128886
URI
https://basepub.dauphine.fr/handle/123456789/20887
Collections
  • CEREMADE : Publications
Metadata
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Author
Gontier, David
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
In this article, we study Schrödinger operators on the real line, when the external potential represents a dislocation in a periodic medium. We study how the spectrum varies with the dislocation parameter. We introduce several integer-valued indices, including the Chern number for bulk indices, and various spectral flows for edge indices. We prove that all these indices coincide, providing a proof of a bulk-edge correspondence in this case. The study is also made for dislocations in Dirac models on the real line. We prove that 0 is always an eigenvalue of such operators.

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