Ballistic Transport for the Schrödinger Operator with Limit-Periodic or Quasi-periodic Potential in Dimension Two

We prove the existence of ballistic transport for the Schr\"odinger operator with limit-periodic or quasi-periodic potential in dimension two. This is done under certain regularity assumptions on the potential which have been used in prior work to establish the existence of an absolutely contin...

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Bibliographic Details
Published inarXiv.org
Main Authors Karpeshina, Yulia, Young-Ran, Lee, Shterenberg, Roman, Stolz, Günter
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.10.2016
Subjects
Eigenvalues
Eigenvectors
Lower bounds
Operators (mathematics)
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Summary:We prove the existence of ballistic transport for the Schr\"odinger operator with limit-periodic or quasi-periodic potential in dimension two. This is done under certain regularity assumptions on the potential which have been used in prior work to establish the existence of an absolutely continuous component and other spectral properties. The latter include detailed information on the structure of generalized eigenvalues and eigenfunctions. These allow to establish the crucial ballistic lower bound through integration by parts on an appropriate extension of a Cantor set in momentum space, as well as through stationary phase arguments.
ISSN:2331-8422
DOI:10.48550/arxiv.1507.06523