
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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Article accepté pour publication ou publiéDate
2020-04Journal name
Journal of Mathematical PhysicsVolume
61Number
4Publisher
American Institute of Physics
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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 operatorsRelated items
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