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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">10.17586/2220-8054-2015-6-2-173-181</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-905</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>PAPERS, PRESENTED AT THE CONFERENCE</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>PAPERS, PRESENTED AT THE CONFERENCE</subject></subj-group></article-categories><title-group><article-title>Time-dependent quantum graph</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>Matrasulov</surname><given-names>D. U.</given-names></name></name-alternatives><bio xml:lang="en"><p>17. Niyazov Str., 100095, Tashkent</p><p>100174, Tashkent</p></bio><email xlink:type="simple">dmatrasulov@gmail.com</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>Yusupov</surname><given-names>J. R.</given-names></name></name-alternatives><bio xml:lang="en"><p>17. Niyazov Str., 100095, Tashkent</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Sabirov</surname><given-names>K. K.</given-names></name></name-alternatives><bio xml:lang="en"><p>100174, Tashkent</p></bio><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Sobirov</surname><given-names>Z. A.</given-names></name></name-alternatives><bio xml:lang="en"><p>100174, Tashkent</p><p>60A, Amir Temur Str., 100000, Tashkent</p></bio><xref ref-type="aff" rid="aff-4"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>Turin Polytechnic University in Tashkent; National University of Uzbekistan</institution><country>Uzbekistan</country></aff><aff xml:lang="en" id="aff-2"><institution>Turin Polytechnic University in Tashkent</institution><country>Uzbekistan</country></aff><aff xml:lang="en" id="aff-3"><institution>National University of Uzbekistan</institution><country>Uzbekistan</country></aff><aff xml:lang="en" id="aff-4"><institution>National University of Uzbekistan; Tashkent Financial Institute</institution><country>Uzbekistan</country></aff><pub-date pub-type="collection"><year>2015</year></pub-date><pub-date pub-type="epub"><day>14</day><month>08</month><year>2025</year></pub-date><volume>6</volume><issue>2</issue><fpage>173</fpage><lpage>181</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Matrasulov D.U., Yusupov J.R., Sabirov K.K., Sobirov Z.A., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Matrasulov D.U., Yusupov J.R., Sabirov K.K., Sobirov Z.A.</copyright-holder><copyright-holder xml:lang="en">Matrasulov D.U., Yusupov J.R., Sabirov K.K., Sobirov Z.A.</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/905">https://nanojournal.ifmo.ru/jour/article/view/905</self-uri><abstract><p>In this paper, we study quantum star graphs with time-dependent bond lengths. Quantum dynamics are treated by solving Schrodinger equation with time-dependent boundary conditions given on graphs. The time-dependence of the average kinetic energy is analyzed. The space-time evolution of a Gaussian wave packet is treated for an harmonically breathing star graph.</p></abstract><kwd-group xml:lang="en"><kwd>quantum graph</kwd><kwd>time-dependent boundary conditions</kwd><kwd>wave packet dynamics</kwd></kwd-group><funding-group><funding-statement xml:lang="en">This work was supported in part by a research grant of Third World Academy of Sciences (Ref. 12-144RG/PHYS/AS G).</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">Kottos T. and Smilansky U. Periodic Orbit Theory and Spectral Statistics for Quantum Graphs. Ann.Phys., 274(1), P.76–124 (1999).</mixed-citation><mixed-citation xml:lang="en">Kottos T. and Smilansky U. 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