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Singular Continuous Spectrum for a Class of Substitution Hamiltonians II

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
Related URLs:
URLURL TypeDescription
https://doi.org/10.1023/a:1007697301341DOIArticle
https://rdcu.be/b3i0fPublisherFree Readcube Access
ORCID:
AuthorORCID
Damanik, David0000-0001-5924-3849
Additional Information:© 2000 Kluwer Academic Publishers. Received: 9 May 2000. This work was supported by the German Academic Exchange Service through Hochschulsonderprogramm III (Postdoktoranden).
Funders:
Funding AgencyGrant Number
Deutscher Akademischer Austauschdienst (DAAD)UNSPECIFIED
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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