Spectral properties of Schrödinger operators associated to almost minimal substitution systems
Benjamin Eichinger,
Philipp Gohlke
Abstract:We study the spectral properties of ergodic Schrödinger 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 characterize… Show more
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