On the Spectrum of Quasi-periodic Schrödinger Operators on Zd with C2-Cosine Type Potentials

In this paper, we establish the Anderson localization, strong dynamical localization and the ( 1 2 - ) -Hölder continuity of the integrated density of states (IDS) for some multi-dimensional discrete quasi-periodic (QP) Schrödinger operators with asymmetric C 2 -cosine type potentials. We extend bot...

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Bibliographic Details
Published in:Communications in mathematical physics 2024, Vol.405 (8)
Main Authors: Cao, Hongyi, Shi, Yunfeng, Zhang, Zhifei
Format: Article
Language:English
Subjects:
Anderson localization
Asymmetry
Classical and Quantum Gravitation
Complex Systems
Continuity (mathematics)
Mathematical and Computational Physics
Mathematical Physics
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:In this paper, we establish the Anderson localization, strong dynamical localization and the ( 1 2 - ) -Hölder continuity of the integrated density of states (IDS) for some multi-dimensional discrete quasi-periodic (QP) Schrödinger operators with asymmetric C 2 -cosine type potentials. We extend both the iteration scheme of Cao-Shi-Zhang (Commun Math Phys 404(1):495–561, 2023) and the interlacing method of Forman and VandenBoom (Localization and Cantor spectrum for quasiperiodic discrete Schrödinger operators with asymmetric, smooth, cosine-like sampling functions. arXiv:2107.05461 , 2021) to handle asymmetric Rellich functions with collapsed gaps .
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-024-05073-9