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Mixed spectral types for the one-frequency discrete quasi-periodic Schrödinger operator


Author: Shiwen Zhang
Journal: Proc. Amer. Math. Soc. 144 (2016), 2603-2609
MSC (2010): Primary 37A30, 47B36, 82B44
DOI: https://doi.org/10.1090/proc/12929
Published electronically: October 19, 2015
MathSciNet review: 3477077
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Abstract: We consider a family of one-frequency discrete analytic quasi-periodic Schrödinger operators. We show that this family provides an example of coexistence of absolutely continuous and point spectrum for some parameters as well as coexistence of absolutely continuous and singular continuous spectrum for some other parameters.


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Additional Information

Shiwen Zhang
Affiliation: Department of Mathematics, University of California Irvine, Irvine, California 92617
Email: shiwez1@uci.edu

DOI: https://doi.org/10.1090/proc/12929
Keywords: Quasi-periodic Schr\"odinger operators, mixed spectral types, Lyapunov exponent, almost reducibility
Received by editor(s): April 24, 2015
Received by editor(s) in revised form: August 5, 2015
Published electronically: October 19, 2015
Additional Notes: This research was partially supported by NSF DMS-1401204
Communicated by: Michael Hitrik
Article copyright: © Copyright 2015 American Mathematical Society