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Log-dimensional spectral properties of one-dimensional quasicrystals

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.

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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.

Item Type:Article
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Damanik, David0000-0001-5924-3849
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.
Funding AgencyGrant Number
National Science FoundationDMS-0010101
National Science FoundationDMS-0070755
Subject Keywords:Schrödinger operators; Hausdorff dimensional spectral properties; Sturmian potentials
Issue or Number:7
Record Number:CaltechAUTHORS:DAMpams03
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12270
Deposited By: Tony Diaz
Deposited On:13 Nov 2008 03:16
Last Modified:08 Nov 2021 22:27

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