Discrete Schrödinger operators with decaying and oscillating potentials
Journal article, 2024
The paper is devoted to a family of discrete one-dimensional Schrödinger operators with power-like decaying potentials with rapid oscillations. In particular, for the potential V (n) = λn−α cos(πωnβ) with 1 < β < 2α, it is proved that the spectrum is purely absolutely continuous on the spectrum of the Laplacian.
Spectrum
Laplacian
almost Mathieu operator
Author
Rupert L. Frank
Munich Ctr Quantum Sci & Technol MCQST
Ludwig Maximilian University of Munich (LMU)
California Institute of Technology (Caltech)
Simon Larson
Chalmers, Mathematical Sciences, Algebra and geometry
St. Petersburg Mathematical Journal
1061-0022 (ISSN) 1547-7371 (eISSN)
Vol. 35 1 233-244Subject Categories
Atom and Molecular Physics and Optics
Mathematical Analysis
DOI
10.1090/spmj/1803