Schroedinger operators with Rudin-Shapiro potentials are not palindromic

Journal Article · Tue Apr 01 00:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531916· OSTI ID:527841

Allouche, J ^[1]

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1. CNRS, LRI, Batiment 490, F-91405 Orsay Cedex (France)

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.}

• OSTI ID: 527841
• Journal Information: Journal of Mathematical Physics, Vol. 38, Issue 4; Other Information: PBD: Apr 1997
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
QUANTUM OPERATORS
SCHROEDINGER PICTURE
MATHEMATICAL OPERATORS
POTENTIALS
SPECTRA
QUANTUM MECHANICS