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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">10.17586/2220-8054-2022-13-6-628-631</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-276</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="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Master equation for correlators of normal-ordered field mode operators</article-title><trans-title-group xml:lang="ru"><trans-title>Основное уравнение для корреляторов нормально упорядоченных полевых операторов</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><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><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><email xlink:type="simple">alextrifanov@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Университет ИТМО</institution></aff><aff xml:lang="en"><institution>ITMO University</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>06</day><month>06</month><year>2025</year></pub-date><volume>13</volume><issue>6</issue><fpage>628</fpage><lpage>631</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/276">https://nanojournal.ifmo.ru/jour/article/view/276</self-uri><abstract><p>We study the master equation for open quantum systems in the alternative form, preserving the normal form of the averaged normal-ordered operators. We give an example of using this equation for the correlators of normal-ordered field mode operators. We explore the properties of the system of linear equations for the higher-order field operators based on the example of a two-mode bosonic system.</p></abstract><trans-abstract xml:lang="ru"><p>Мы изучаем основное уравнение открытых квантовых систем в альтернативной форме, сохраняющей нормальную форму усредненных нормально упорядоченных операторов. Мы даем пример использования этого уравнения для корреляторов нормально упорядоченных полевых операторов. Мы исследуем свойства системы линейных уравнений, основываясь на примере двухмодовой бозонной системы.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>основное уравнение</kwd><kwd>нормально-упорядоченные операторы</kwd><kwd>двухмодовая бозонная система</kwd></kwd-group><kwd-group xml:lang="en"><kwd>master equation</kwd><kwd>normal-ordered correlators</kwd><kwd>two-mode bosonic system</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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