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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2018-9-2-162-170</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-635</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MATHEMATICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>МАТЕМАТИКА</subject></subj-group></article-categories><title-group><article-title>Solvable models of quantum beating</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Carlone</surname><given-names>R.</given-names></name></name-alternatives><bio xml:lang="en"><p>MSA, via Cinthia, I-80126, Napoli</p></bio><email xlink:type="simple">raffaele.carlone@unina.it</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Figari</surname><given-names>R.</given-names></name></name-alternatives><bio xml:lang="en"><p>MSA, via Cinthia, I-80126, Napoli</p></bio><email xlink:type="simple">rodolfo.figari@na.infn.it</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Negulescu</surname><given-names>C.</given-names></name></name-alternatives><bio xml:lang="en"><p>UMR 5219´ F-31062 Toulouse</p></bio><email xlink:type="simple">claudia.negulescu@math.univ-toulouse.fr</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Tentarelli</surname><given-names>L.</given-names></name></name-alternatives><bio xml:lang="en"><p>Piazzale Aldo Moro, 5, 00185, Roma</p></bio><email xlink:type="simple">tentarelli@mat.uniroma1.it</email><xref ref-type="aff" rid="aff-4"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>Universita “Federico II” di Napoli, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”</institution><country>Italy</country></aff><aff xml:lang="en" id="aff-2"><institution>Universita “Federico II” di Napoli, Dipartimento di Fisica e INFN Sezione di Napoli</institution><country>Italy</country></aff><aff xml:lang="en" id="aff-3"><institution>Universite de Toulouse &amp; CNRS, UPS, Institut de Math´ematiques de Toulouse</institution><country>France</country></aff><aff xml:lang="en" id="aff-4"><institution>Sapienza Universita di Roma, Dipartimento di Matematica</institution><country>Italy</country></aff><pub-date pub-type="collection"><year>2018</year></pub-date><pub-date pub-type="epub"><day>12</day><month>08</month><year>2025</year></pub-date><volume>9</volume><issue>2</issue><elocation-id>162–170</elocation-id><permissions><copyright-statement>Copyright &amp;#x00A9; Carlone R., Figari R., Negulescu C., Tentarelli L., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Carlone R., Figari R., Negulescu C., Tentarelli L.</copyright-holder><copyright-holder xml:lang="en">Carlone R., Figari R., Negulescu C., Tentarelli L.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/635">https://nanojournal.ifmo.ru/jour/article/view/635</self-uri><abstract><p>We review some results about the suppression of quantum beating in a one dimensional nonlinear double well potential. We implement a single particle double well potential model, making use of nonlinear point interactions. We show that there is complete suppression of the typical beating phenomenon characterizing the linear quantum case.</p></abstract><kwd-group xml:lang="en"><kwd>nonlinear Schrodinger equation</kwd><kwd>weakly singular Volterra integral equations</kwd><kwd>quantum beating</kwd></kwd-group><funding-group><funding-statement xml:lang="en">R.C. and L.T. acknowledge the support of the FIR 2013 project “Condensed Matter in Mathematical Physics”, Ministry of University and Research of Italian Republic (code RBFR13WAET). C.N. would like to acknowledge support from the CNRS-PICS project “MANUS” (Modelling and Numerics of Spintronics and Graphenes, 2016 – 2018).</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Davies E.B. 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