{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T07:39:25Z","timestamp":1790753965818,"version":"4.1.0"},"reference-count":18,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,5]],"date-time":"2023-01-05T00:00:00Z","timestamp":1672876800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["N19-12-00167"],"award-info":[{"award-number":["N19-12-00167"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We analyze the classical and quantum dynamics of the driven dissipative Bose\u2013Hubbard dimer. Under variation of the driving frequency, the classical system is shown to exhibit a bifurcation to the limit cycle, where its steady-state solution corresponds to periodic oscillation with the frequency unrelated to the driving frequency. This bifurcation is shown to lead to a peculiarity in the stationary single-particle density matrix of the quantum system. The case of the Bose\u2013Hubbard trimer, where the discussed limit cycle bifurcates into a chaotic attractor, is briefly discussed.<\/jats:p>","DOI":"10.3390\/e25010117","type":"journal-article","created":{"date-parts":[[2023,1,6]],"date-time":"2023-01-06T01:48:19Z","timestamp":1672969699000},"page":"117","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quantum Manifestation of the Classical Bifurcation in the Driven Dissipative Bose\u2013Hubbard Dimer"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3155-2997","authenticated-orcid":false,"given":"Pavel","family":"Muraev","sequence":"first","affiliation":[{"name":"Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk, Russia"},{"name":"School of Engineering Physics and Radio Electronics, Siberian Federal University, 660041 Krasnoyarsk, Russia"},{"name":"IRC SQC, Siberian Federal University, 660041 Krasnoyarsk, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dmitrii","family":"Maksimov","sequence":"additional","affiliation":[{"name":"Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk, Russia"},{"name":"IRC SQC, Siberian Federal University, 660041 Krasnoyarsk, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5072-8126","authenticated-orcid":false,"given":"Andrey","family":"Kolovsky","sequence":"additional","affiliation":[{"name":"Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk, Russia"},{"name":"School of Engineering Physics and Radio Electronics, Siberian Federal University, 660041 Krasnoyarsk, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4950","DOI":"10.1103\/PhysRevLett.79.4950","article-title":"Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates","volume":"79","author":"Smerzi","year":"1997","journal-title":"Phys. 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E"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/117\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:00:36Z","timestamp":1760119236000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/117"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,5]]},"references-count":18,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["e25010117"],"URL":"https:\/\/doi.org\/10.3390\/e25010117","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,5]]}}}