Spectral Properties of Schrodinger Operators Associated with Almost Minimal Substitution Systems

Eichinger B, Gohlke P (2020)
Annales Henri Poincaré.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Eichinger, Benjamin; Gohlke, PhilippUniBi
Abstract / Bemerkung
We study the spectral properties of ergodic Schrodinger operators that are associated with a certain family of non-primitive substitutions on a binary alphabet. The corresponding subshifts provide examples of dynamical systems that go beyond minimality, unique ergodicity and linear complexity. In some parameter region, we are naturally in the setting of an infinite ergodic measure. The almost sure spectrum is singular and contains an interval. We show that under certain conditions, eigenvalues can appear. Some criteria for the exclusion of eigenvalues are fully characterized, including the existence of strongly palindromic sequences. Many of our structural insights rely on return word decompositions in the context of non-uniformly recurrent sequences. We introduce an associated induced system that is conjugate to an odometer.
Stichworte
Schrö; dinger operators; Non-primitive substitutions
Erscheinungsjahr
2020
Zeitschriftentitel
Annales Henri Poincaré
ISSN
1424-0637
eISSN
1424-0661
Page URI
https://pub.uni-bielefeld.de/record/2948931

Zitieren

Eichinger B, Gohlke P. Spectral Properties of Schrodinger Operators Associated with Almost Minimal Substitution Systems. Annales Henri Poincaré. 2020.
Eichinger, B., & Gohlke, P. (2020). Spectral Properties of Schrodinger Operators Associated with Almost Minimal Substitution Systems. Annales Henri Poincaré. doi:10.1007/s00023-020-00975-5
Eichinger, B., and Gohlke, P. (2020). Spectral Properties of Schrodinger Operators Associated with Almost Minimal Substitution Systems. Annales Henri Poincaré.
Eichinger, B., & Gohlke, P., 2020. Spectral Properties of Schrodinger Operators Associated with Almost Minimal Substitution Systems. Annales Henri Poincaré.
B. Eichinger and P. Gohlke, “Spectral Properties of Schrodinger Operators Associated with Almost Minimal Substitution Systems”, Annales Henri Poincaré, 2020.
Eichinger, B., Gohlke, P.: Spectral Properties of Schrodinger Operators Associated with Almost Minimal Substitution Systems. Annales Henri Poincaré. (2020).
Eichinger, Benjamin, and Gohlke, Philipp. “Spectral Properties of Schrodinger Operators Associated with Almost Minimal Substitution Systems”. Annales Henri Poincaré (2020).

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