Document Zbl 07957801

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Spectr. Theory</a> <a href="/?q=in%3A521606" title="Articles in this Issue">14, No. 4, 1513-1536 (2024)</a>. </div> <div class="abstract">Summary: We give a criterion based on reflection symmetries in the spirit of Jitomirskaya-Simon to show absence of point spectrum for (split-step) quantum walks and Cantero-Moral-Velázquez (CMV) matrices. To accomplish this, we use some ideas from a recent paper by the authors and collaborators to implement suitable reflection symmetries for such operators. We give several applications. For instance, we deduce arithmetic delocalization in the phase for the unitary almost-Mathieu operator and singular continuous spectrum for generic CMV matrices generated by the Thue-Morse subshift.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7957801">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A47B93" title="MSC2020">47B93</a> </td> <td class="space"> Operators arising in mathematical physics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47A10" title="MSC2020">47A10</a> </td> <td class="space"> Spectrum, resolvent </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47B36" title="MSC2020">47B36</a> </td> <td class="space"> Jacobi (tridiagonal) operators (matrices) and generalizations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A58J51" title="MSC2020">58J51</a> </td> <td class="space"> Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A81Q10" title="MSC2020">81Q10</a> </td> <td class="space"> Selfadjoint operator theory in quantum theory, including spectral analysis </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aunitary+almost+Mathieu+operator">unitary almost Mathieu operator</a>; <a href="/?q=ut%3Asingular+continuous+spectrum">singular continuous spectrum</a>; <a href="/?q=ut%3Aresonances">resonances</a>; <a href="/?q=ut%3Aquantum+walks">quantum walks</a>; <a href="/?q=ut%3ACMV+matrices">CMV matrices</a>; <a href="/?q=ut%3Adelocalization">delocalization</a>; <a href="/?q=ut%3Aquasi-periodicity">quasi-periodicity</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07957801" data-ciurl="/ci/07957801" data-biburl="/bibtex/07957801.bib" data-amsurl="/amsrefs/07957801.bib" data-xmlurl="/xml/07957801.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07957801.pdf" title="Zbl 07957801 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.4171/JST/533" aria-label="DOI for “Absence of bound states for quantum walks and CMV matrices via reflections”" title="10.4171/JST/533">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2402.11024"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">A. 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