Log-dimensional spectral properties of one-dimensional quasicrystals
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- by David Damanik and Michael Landrigan PDF
- Proc. Amer. Math. Soc. 131 (2003), 2209-2216 Request permission
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.References
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Additional Information
- David Damanik
- Affiliation: Department of Mathematics 253–37, California Institute of Technology, Pasadena, California 91125
- MR Author ID: 621621
- Email: damanik@its.caltech.edu
- Michael Landrigan
- Affiliation: Department of Mathematics, Idaho State University, Pocatello, Idaho 83209
- Email: landmich@isu.edu
- 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
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1963769