{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T00:50:33Z","timestamp":1776127833288,"version":"3.50.1"},"reference-count":99,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,4]],"date-time":"2022-10-04T00:00:00Z","timestamp":1664841600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004329","name":"Slovenian Research Agency (ARRS)","doi-asserted-by":"publisher","award":["J1-9112"],"award-info":[{"award-number":["J1-9112"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Slovenian Research Agency (ARRS)","doi-asserted-by":"publisher","award":["11805165"],"award-info":[{"award-number":["11805165"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Slovenian Research Agency (ARRS)","doi-asserted-by":"publisher","award":["LY20A050001"],"award-info":[{"award-number":["LY20A050001"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["J1-9112"],"award-info":[{"award-number":["J1-9112"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["11805165"],"award-info":[{"award-number":["11805165"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["LY20A050001"],"award-info":[{"award-number":["LY20A050001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Nature Science Foundation","doi-asserted-by":"publisher","award":["J1-9112"],"award-info":[{"award-number":["J1-9112"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Nature Science Foundation","doi-asserted-by":"publisher","award":["11805165"],"award-info":[{"award-number":["11805165"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Nature Science Foundation","doi-asserted-by":"publisher","award":["LY20A050001"],"award-info":[{"award-number":["LY20A050001"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We systematically study the chaotic signatures in a quantum many-body system consisting of an ensemble of interacting two-level atoms coupled to a single-mode bosonic field, the so-called extended Dicke model. The presence of the atom\u2013atom interaction also leads us to explore how the atomic interaction affects the chaotic characters of the model. By analyzing the energy spectral statistics and the structure of eigenstates, we reveal the quantum signatures of chaos in the model and discuss the effect of the atomic interaction. We also investigate the dependence of the boundary of chaos extracted from both eigenvalue-based and eigenstate-based indicators on the atomic interaction. We show that the impact of the atomic interaction on the spectral statistics is stronger than on the structure of eigenstates. Qualitatively, the integrablity-to-chaos transition found in the Dicke model is amplified when the interatomic interaction in the extended Dicke model is switched on.<\/jats:p>","DOI":"10.3390\/e24101415","type":"journal-article","created":{"date-parts":[[2022,10,8]],"date-time":"2022-10-08T04:04:56Z","timestamp":1665201896000},"page":"1415","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Quantum Chaos in the Extended Dicke Model"],"prefix":"10.3390","volume":"24","author":[{"given":"Qian","family":"Wang","sequence":"first","affiliation":[{"name":"CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000 Maribor, Slovenia"},{"name":"Department of Physics, Zhejiang Normal University, Jinhua 321004, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"073601","DOI":"10.1103\/PhysRevLett.108.073601","article-title":"Quantum Chaos and Effective Thermalization","volume":"108","author":"Altland","year":"2012","journal-title":"Phys. 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