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. doi:10.1103/PhysRevLett.76.1765. https://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 | ||||||
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| 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 | ||||||
| Issue or Number: | 11 | ||||||
| DOI: | 10.1103/PhysRevLett.76.1765 | ||||||
| Record Number: | CaltechAUTHORS:JITprl96 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:JITprl96 | ||||||
| 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: | 08 Nov 2021 20:29 |
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