Discrete Schrödinger operators with decaying and oscillating potentials
- Creators
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Frank, Rupert L.1, 2, 3
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Larson, Simon4
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1.
Ludwig-Maximilians-Universität München
- 2. Munich Center for Quantum Science and Technology
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3.
California Institute of Technology
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4.
Chalmers University of Technology
Abstract
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(πωn^β) with 1<β<2α, it is proved that the spectrum is purely absolutely continuous on the spectrum of the Laplacian.
Copyright and License
© 2024 American Mathematical Society.
Acknowledgement
The first author is grateful to J. Breuer and H. Krüger for discussions on the topic of
this paper.
Funding
Partial support through U.S. National Science Foundation grants DMS-1363432 and DMS-1954995 (R.L.F.), through the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), through Germany’s Excellence Strategy EXC–2111–390814868 (R.L.F.), and through Knut and Alice Wallenberg Foundation grant KAW 2018.0281 and KAW 2021.0193 (S.L.) is acknowledged.
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Additional details
- National Science Foundation
- DMS-1363432
- National Science Foundation
- DMS-1954995
- Deutsche Forschungsgemeinschaft (DFG)
- EXC-2111-390814868
- Knut and Alice Wallenberg Foundation
- KAW 2018.0281
- Knut and Alice Wallenberg Foundation
- KAW 2021.0193
- Available
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2024-04-12Published electronically
- Publication Status
- Published