Log-dimensional spectral properties of one-dimensional quasicrystals

Authors:
David Damanik and Michael Landrigan

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2209-2216

MSC (2000):
Primary 81Q10, 47B80

DOI:
https://doi.org/10.1090/S0002-9939-02-06747-3

Published electronically:
November 6, 2002

MathSciNet review:
1963769

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Abstract | References | Similar Articles | Additional Information

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

**David Damanik**

Affiliation:
Department of Mathematics 253–37, California Institute of Technology, Pasadena, California 91125

Email:
damanik@its.caltech.edu

**Michael Landrigan**

Affiliation:
Department of Mathematics, Idaho State University, Pocatello, Idaho 83209

Email:
landmich@isu.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06747-3

Keywords:
Schr\"odinger operators,
Hausdorff dimensional spectral properties,
Sturmian potentials

Received by editor(s):
October 5, 2001

Received by editor(s) in revised form:
February 23, 2002

Published electronically:
November 6, 2002

Additional Notes:
The first author was supported in part by the National Science Foundation through Grant DMS–0010101

The second author was supported in part by the National Science Foundation through Grant DMS-0070755

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2002
American Mathematical Society