TL;DR
This paper presents criteria to determine palindromicity in bi-infinite sequences and offers a method to construct palindromic minimal sequences, linking them to spectral properties of certain quantum models.
Contribution
It introduces a simple criterion for excluding palindromicity and a constructive method for building palindromic sequences using regular model sets.
Findings
Criterion effectively excludes palindromicity in minimal sequences.
Constructed sequences relate to models with purely singular continuous spectrum.
Application to Rudin-Shapiro sequence demonstrates practical relevance.
Abstract
Two results on palindromicity of bi-infinite words in a finite alphabet are presented. The first is a simple, but efficient criterion to exclude palindromicity of minimal sequences and applies, in particular, to the Rudin-Shapiro sequence. The second provides a constructive method to build palindromic minimal sequences based upon regular, generic model sets with centro-symmetric window. These give rise to diagonal tight-binding models in one dimension with purely singular continuous spectrum.
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