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Dimensional Hausdorff properties of singular continuous spectra

Jitomirskaya, Svetlana Ya. and Last, Yoram (1996) Dimensional Hausdorff properties of singular continuous spectra. Physical Review Letters, 76 (11). pp. 1765-1769. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:JITprl96

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Abstract

We present an extension of the Gilbert-Pearson theory of subordinacy, which relates dimensional Hausdorff spectral properties of one-dimensional Schrödinger operators to the behavior of solutions of the corresponding Schrödinger equation. We use this theory to analyze these properties for several examples having the singular-continuous spectrum, including sparse barrier potentials, the almost Mathieu operator and the Fibonacci Hamiltonian.


Item Type:Article
Additional Information:©1996 The American Physical Society. Received 19 October 1995. We would like to thank J. Avron and B. Simon for useful discussions. This research was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation, and by the Erwin Schrödinger Institute (Vienna) where part of this work was done. The work of S.J. was supported in part by NSF Grants DMS-9208029 and DMS-9501265.
Subject Keywords:PURE POINT SPECTRUM; SCHRODINGER-OPERATORS; JACOBI MATRICES; QUANTUM-SYSTEMS; SUBORDINACY; ABSENCE
Record Number:CaltechAUTHORS:JITprl96
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:JITprl96
Alternative URL:http://dx.doi.org/10.1103/PhysRevLett.76.1765
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5818
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:03 Nov 2006
Last Modified:26 Dec 2012 09:15

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