Spectral Properties of Schrödinger Operators Associated with Almost Minimal Substitution Systems
| Autor: | Benjamin Eichinger, Philipp Gohlke |
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| Rok vydání: | 2020 |
| Předmět: |
Nuclear and High Energy Physics
Pure mathematics Mathematics::Dynamical Systems 37B10 Dynamical systems theory Context (language use) 01 natural sciences Measure (mathematics) 81Q10 37B10 52C23 0103 physical sciences Ergodic theory Mathematics - Dynamical Systems 0101 mathematics Schrödinger operators Mathematical Physics Eigenvalues and eigenvectors Mathematics Original Paper 010102 general mathematics Spectrum (functional analysis) Ergodicity Substitution (algebra) dinger operators Statistical and Nonlinear Physics 52C23 81Q10 Non-primitive substitutions 010307 mathematical physics Schrö |
| Zdroj: | Annales Henri Poincare |
| ISSN: | 1424-0661 |
| Popis: | We study the spectral properties of ergodic Schr\"{o}dinger operators that are associated to 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. 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. Comment: Included a result on eigenvalues, added another case distinction (Erratum) |
| Databáze: | OpenAIRE |
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