Damanik, David and Landrigan, Michael (2003) Log-dimensional spectral properties of one-dimensional quasicrystals. Proceedings of the American Mathematical Society, 131 (7). pp. 2209-2216. ISSN 0002-9939. doi:10.1090/S0002-9939-02-06747-3. https://resolver.caltech.edu/CaltechAUTHORS:DAMpams03
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Abstract
We consider discrete one-dimensional Schrödinger operators on the whole line and establish a criterion for continuity of spectral measures with respect to log-Hausdorff measures. We apply this result to operators with Sturmian potentials and thereby prove logarithmic quantum dynamical lower bounds for all coupling constants and almost all rotation numbers, uniformly in the phase.
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| Additional Information: | © 2003 American Mathematical Society. Communicated by Joseph A. Ball. Received by the editors October 5, 2001 and, in revised form, February 23, 2002. Article electronically published on November 6, 2002. The first author [D.D.] was supported in part by the National Science Foundation through Grant DMS-0010101. The second author [M.L.] was supported in part by the National Science Foundation through Grant DMS-0070755. | |||||||||
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| Subject Keywords: | Schrödinger operators; Hausdorff dimensional spectral properties; Sturmian potentials | |||||||||
| Issue or Number: | 7 | |||||||||
| DOI: | 10.1090/S0002-9939-02-06747-3 | |||||||||
| Record Number: | CaltechAUTHORS:DAMpams03 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:DAMpams03 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 12270 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 13 Nov 2008 03:16 | |||||||||
| Last Modified: | 08 Nov 2021 22:27 |
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