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Edge states in ordinary differential equations for dislocations

Gontier, David (2020), Edge states in ordinary differential equations for dislocations, Journal of Mathematical Physics, 61, 4. 10.1063/1.5128886

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Type
Article accepté pour publication ou publié
Date
2020-04
Journal name
Journal of Mathematical Physics
Volume
61
Number
4
Publisher
American Institute of Physics
Publication identifier
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Author(s)
Gontier, David cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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.
Subjects / Keywords
Operator theory; Functional analysis; Hellmann Feynman theorem; Dirac equation; Hill equation; Quantum mechanical operators