The Rotation Number for Almost Periodic Potentials with Jump Discontinuities and δ-Interactions

We consider one-dimensional Schrödinger operators with generalized almost periodic potentials with jump discontinuities and δ -interactions. For operators of this kind, we introduce a rotation number in the spirit of Johnson and Moser. To do this, we introduce the concept of almost periodicity at a...

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Bibliographic Details
Published inAnnales Henri Poincaré Vol. 25; no. 2; pp. 1359 - 1397
Main Authors Damanik, David, Zhang, Meirong, Zhou, Zhe
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2024
Springer Nature B.V
Subjects
Classical and Quantum Gravitation
Discontinuity
Dynamical Systems and Ergodic Theory
Elementary Particles
Mathematical and Computational Physics
Mathematical Methods in Physics
Operators (mathematics)
Periodic functions
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Rotation
Theoretical
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Summary:We consider one-dimensional Schrödinger operators with generalized almost periodic potentials with jump discontinuities and δ -interactions. For operators of this kind, we introduce a rotation number in the spirit of Johnson and Moser. To do this, we introduce the concept of almost periodicity at a rather general level, and then the almost periodic function with jump discontinuities and δ -interactions as an application.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-023-01404-z