Limit-periodic Schrödinger operators with a discontinuous Lyapunov exponent

We construct a limit-periodic Schrödinger operator for which the Lyapunov exponent has a positive measure set of discontinuities. We also show that the limit-periodic potentials for which the Lyapunov exponent is discontinuous are dense in the space of limit-periodic potentials.

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Bibliographic Details
Published inJournal of functional analysis Vol. 279; no. 4; p. 108565
Main Authors Damanik, David, Gan, Zheng, Krüger, Helge
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2020
Subjects
Limit-periodic potential
Lyapunov exponent
Schrödinger operator
Limit-periodic potential
Schrödinger operator
Lyapunov exponent
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Summary:We construct a limit-periodic Schrödinger operator for which the Lyapunov exponent has a positive measure set of discontinuities. We also show that the limit-periodic potentials for which the Lyapunov exponent is discontinuous are dense in the space of limit-periodic potentials.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2020.108565