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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">10.17586/2220-8054-2023-14-2-626-632</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-139</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>PHYSICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group></article-categories><title-group><article-title>Hidden polarization in open quantum systems</article-title><trans-title-group xml:lang="ru"><trans-title>Скрытая поляризация в открытых квантовых системах</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-1853-2171</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ватутин</surname><given-names>А. Д.</given-names></name><name name-style="western" xml:lang="en"><surname>Vatutin</surname><given-names>A. D.</given-names></name></name-alternatives><bio xml:lang="en"><p>Alexander D. Vatutin</p><p>Kronverkskiy 49, St.-Petersburg</p></bio><email xlink:type="simple">advatutin@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-4265-8818</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мирошниченко</surname><given-names>Г. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Miroshnichenko</surname><given-names>G. P.</given-names></name></name-alternatives><bio xml:lang="en"><p>George P. Miroshnichenko</p><p>Kronverkskiy 49, St.-Petersburg</p></bio><email xlink:type="simple">gpmirosh@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5109-2086</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Трифанов</surname><given-names>А. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Trifanov</surname><given-names>A. I.</given-names></name></name-alternatives><bio xml:lang="en"><p>Alexander I. Trifanov</p><p>Kronverkskiy 49, St.-Petersburg</p></bio><email xlink:type="simple">alextrifanov@itmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>ITMO University</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2023</year></pub-date><pub-date pub-type="epub"><day>02</day><month>06</month><year>2025</year></pub-date><volume>14</volume><issue>6</issue><fpage>626</fpage><lpage>632</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Vatutin A.D., Miroshnichenko G.P., Trifanov A.I., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Ватутин А.Д., Мирошниченко Г.П., Трифанов А.И.</copyright-holder><copyright-holder xml:lang="en">Vatutin A.D., Miroshnichenko G.P., Trifanov A.I.</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/139">https://nanojournal.ifmo.ru/jour/article/view/139</self-uri><abstract><p>In this work, we explore the master equation governing open quantum systems dynamics in an alternative form, which preserves the normal-ordered representation of the averaged normal-ordered operators. We derive a linear system of differential equations for the fourth-order moments of corresponding bosonic operators. Polarization moments of the first and the second orders are investigated using plane rotation transformation. We also evaluate the dynamics of the hidden polarization in comparison with the dynamics of usual polarization within open quantum dynamics.</p></abstract><trans-abstract xml:lang="ru"><p>Мы исследуем главное уравнение, задающее открытые квантовые системы, в альтернативной форме, сохраняющее нормально-упорядоченное представление усредненных операторов в нормальной форме. Выведена линейная система дифференциальных уравнений для моментов четвертого порядка. Мы рассматриваем скрытую поляризацию и обычную поляризацию через вращение пластины. Мы оцениваем динамику скрытой поляризации по сравнению с динамикой обычной поляризации в открытых квантовых системах.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>Основное уравнение</kwd><kwd>нормально-упорядоченные операторы</kwd><kwd>скрытая поляризация</kwd><kwd>моменты четвертого порядка</kwd></kwd-group><kwd-group xml:lang="en"><kwd>master equation</kwd><kwd>normal-ordered correlators</kwd><kwd>hidden polarization</kwd><kwd>fourth-order moments</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Pirandola S., Eisert J., Weedbrook C., Furusawa A., Braunstein S.L. Advances in quantum teleportation. Nat. Photon., 2015, 9, P. 641–652.</mixed-citation><mixed-citation xml:lang="en">Pirandola S., Eisert J., Weedbrook C., Furusawa A., Braunstein S.L. Advances in quantum teleportation. Nat. 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