Schroedinger operators with Rudin-Shapiro potentials are not palindromic
Abstract
We prove a conjecture of A. Hof, O. Knill and B. Simon [Commun. Math. Phys. {bold 174}, 149{endash}159 (1995)] by showing that the Rudin-Shapiro sequence is not {ital palindromic}, i.e., does not contain arbitrarily long palindromes. We prove actually this property for all paperfolding sequences and all Rudin-Shapiro sequences deduced from paperfolding sequences. As a consequence and as guessed by the above authors, their method cannot be used for establishing that discrete Schroedinger operators with Rudin-Shapiro potentials have a purely singular continuous spectrum. {copyright} {ital 1997 American Institute of Physics.}
- Authors:
-
- CNRS, LRI, Batiment 490, F-91405 Orsay Cedex (France)
- Publication Date:
- OSTI Identifier:
- 527841
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Mathematical Physics
- Additional Journal Information:
- Journal Volume: 38; Journal Issue: 4; Other Information: PBD: Apr 1997
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 66 PHYSICS; QUANTUM OPERATORS; SCHROEDINGER PICTURE; MATHEMATICAL OPERATORS; POTENTIALS; SPECTRA; QUANTUM MECHANICS
Citation Formats
Allouche, J. Schroedinger operators with Rudin-Shapiro potentials are not palindromic. United States: N. p., 1997.
Web. doi:10.1063/1.531916.
Allouche, J. Schroedinger operators with Rudin-Shapiro potentials are not palindromic. United States. https://doi.org/10.1063/1.531916
Allouche, J. 1997.
"Schroedinger operators with Rudin-Shapiro potentials are not palindromic". United States. https://doi.org/10.1063/1.531916.
@article{osti_527841,
title = {Schroedinger operators with Rudin-Shapiro potentials are not palindromic},
author = {Allouche, J},
abstractNote = {We prove a conjecture of A. Hof, O. Knill and B. Simon [Commun. Math. Phys. {bold 174}, 149{endash}159 (1995)] by showing that the Rudin-Shapiro sequence is not {ital palindromic}, i.e., does not contain arbitrarily long palindromes. We prove actually this property for all paperfolding sequences and all Rudin-Shapiro sequences deduced from paperfolding sequences. As a consequence and as guessed by the above authors, their method cannot be used for establishing that discrete Schroedinger operators with Rudin-Shapiro potentials have a purely singular continuous spectrum. {copyright} {ital 1997 American Institute of Physics.}},
doi = {10.1063/1.531916},
url = {https://www.osti.gov/biblio/527841},
journal = {Journal of Mathematical Physics},
number = 4,
volume = 38,
place = {United States},
year = {Tue Apr 01 00:00:00 EST 1997},
month = {Tue Apr 01 00:00:00 EST 1997}
}
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