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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Spectral Properties of Schrödinger Operators Associated with Almost Minimal Substitution Systems
AU - Eichinger, Benjamin
AU - Gohlke, Philipp
N1 - Publisher Copyright: © 2020, The Author(s).
PY - 2021/5/31
Y1 - 2021/5/31
N2 - We study the spectral properties of ergodic Schrödinger 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.
AB - We study the spectral properties of ergodic Schrödinger 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.
KW - Non-primitive substitutions
KW - Schrödinger operators
U2 - 10.1007/s00023-020-00975-5
DO - 10.1007/s00023-020-00975-5
M3 - Journal article
AN - SCOPUS:85094951554
VL - 22
SP - 1377
EP - 1427
JO - Annales Henri Poincare
JF - Annales Henri Poincare
SN - 1424-0637
IS - 5
ER -