{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T07:00:03Z","timestamp":1788418803962,"version":"build-2803163510"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2015,4,17]],"date-time":"2015-04-17T00:00:00Z","timestamp":1429228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We study the dissipative quantum dynamics and the asymptotic behavior of a particle in a bistable potential interacting with a sub-Ohmic broadband environment. The reduced dynamics, in the intermediate to strong dissipation regime, is obtained beyond the two-level system approximation by using a real-time path integral approach. We find a crossover dynamic regime with damped intra-well oscillations and incoherent tunneling and a completely incoherent regime at strong damping. Moreover, a nonmonotonic behavior of the left\/right well population difference is found as a function of the damping strength.<\/jats:p>","DOI":"10.3390\/e17042341","type":"journal-article","created":{"date-parts":[[2015,4,17]],"date-time":"2015-04-17T11:09:30Z","timestamp":1429268970000},"page":"2341-2354","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":48,"title":["Multi-State Quantum Dissipative Dynamics in Sub-Ohmic Environment: The Strong Coupling Regime"],"prefix":"10.3390","volume":"17","author":[{"given":"Luca","family":"Magazz\u00f9","sequence":"first","affiliation":[{"name":"Dipartimento di Fisica e Chimica, Group of Interdisciplinary Theoretical Physics, Universit\u00e0 di Palermo and CNISM, Unit\u00e0 di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy"},{"name":"Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni Novgorod 603950, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5496-1518","authenticated-orcid":false,"given":"Davide","family":"Valenti","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica e Chimica, Group of Interdisciplinary Theoretical Physics, Universit\u00e0 di Palermo and CNISM, Unit\u00e0 di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4402-2207","authenticated-orcid":false,"given":"Angelo","family":"Carollo","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica e Chimica, Group of Interdisciplinary Theoretical Physics, Universit\u00e0 di Palermo and CNISM, Unit\u00e0 di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernardo","family":"Spagnolo","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica e Chimica, Group of Interdisciplinary Theoretical Physics, Universit\u00e0 di Palermo and CNISM, Unit\u00e0 di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy"},{"name":"Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni Novgorod 603950, Russia"},{"name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, I-90123 Catania, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,4,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1103\/PhysRevLett.46.211","article-title":"Influence of Dissipation on Quantum Tunneling in Macroscopic Systems","volume":"46","author":"Caldeira","year":"1981","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Weiss, U. (2012). Quantum Dissipative Systems, World Scientific. [4th ed.].","DOI":"10.1142\/9789814374927"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"016802","DOI":"10.1103\/PhysRevLett.97.016802","article-title":"Signatures of a Noise-Induced Quantum Phase Transition in a Mesoscopic Metal Ring","volume":"97","author":"Tong","year":"2006","journal-title":"Phys. Rev. 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