Damanik, David (2000) Singular Continuous Spectrum for a Class of Substitution Hamiltonians II. Letters in Mathematical Physics, 54 (1). pp. 25-31. ISSN 0377-9017. doi:10.1023/a:1007697301341. https://resolver.caltech.edu/CaltechAUTHORS:20200330-075735330
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Abstract
We consider discrete one-dimensional Schrödinger operators with aperiodic potentials generated by primitive substitutions. Using the three-block version of Gordon's criterion, we establish purely singular continuous spectrum with probability one provided that the potentials have index greater than three. It is also shown that one cannot use this criterion to prove uniform results.
| Item Type: | Article | |||||||||
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| Additional Information: | © 2000 Kluwer Academic Publishers. Received: 9 May 2000. This work was supported by the German Academic Exchange Service through Hochschulsonderprogramm III (Postdoktoranden). | |||||||||
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| Subject Keywords: | Schrödinger operators; substitution potentials; singular continuous spectrum | |||||||||
| Issue or Number: | 1 | |||||||||
| Classification Code: | MSC 2000: 81Q10, 47B39 | |||||||||
| DOI: | 10.1023/a:1007697301341 | |||||||||
| Record Number: | CaltechAUTHORS:20200330-075735330 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200330-075735330 | |||||||||
| Official Citation: | Damanik, D. Singular Continuous Spectrum for a Class of Substitution Hamiltonians II. Letters in Mathematical Physics 54, 25–31 (2000). https://doi.org/10.1023/A:1007697301341 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 102163 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 30 Mar 2020 15:34 | |||||||||
| Last Modified: | 16 Nov 2021 18:09 |
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