{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T12:15:02Z","timestamp":1754482502788,"version":"3.41.2"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["312057"],"award-info":[{"award-number":["312057"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:p> We discuss the long-time relaxation of a qubit linearly coupled to a finite bath of [Formula: see text] spins (two-level systems, TLSs), with the interaction Hamiltonian in rotating wave approximation. We focus on the regime [Formula: see text], assuming that the qubit\u2013bath coupling is weak, that the range of spin frequencies is sufficiently broad, and that all the spins are initialized in the ground state. Despite the model being perfectly integrable, we make two interesting observations about the effective system relaxation. First, as one would expect, the qubit relaxes exponentially towards its zero-temperature state at a well characterized rate. Second, the bath spins, even when mutually coupled, do not relax towards a thermal distribution, but rather form a Lorentzian distribution peaked at the frequency of the initially excited qubit. This behaviour is captured by an analytical approximation that makes use of the property [Formula: see text] to treat the TLS frequencies as a continuum and is confirmed by our numerical simulations. <\/jats:p>","DOI":"10.1142\/s1230161223500099","type":"journal-article","created":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T09:04:01Z","timestamp":1689584641000},"source":"Crossref","is-referenced-by-count":5,"title":["Long-Time Relaxation of a Finite Spin Bath Linearly Coupled to a Qubit"],"prefix":"10.1142","volume":"30","author":[{"given":"Jukka P.","family":"Pekola","sequence":"first","affiliation":[{"name":"Pico group, QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland"}]},{"given":"Bayan","family":"Karimi","sequence":"additional","affiliation":[{"name":"Pico group, QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland"},{"name":"Helteq group, QTF Centre of Excellence, Department of Physics, University of Helsinki, P.O. Box 43, FI-00014 Helsinki, Finland"}]},{"given":"Marco","family":"Cattaneo","sequence":"additional","affiliation":[{"name":"Pico group, QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland"},{"name":"Algorithmiq Ltd, Kanavakatu 3C 00160 Helsinki, Finland"}]},{"given":"Sabrina","family":"Maniscalco","sequence":"additional","affiliation":[{"name":"Pico group, QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland"},{"name":"Helteq group, QTF Centre of Excellence, Department of Physics, University of Helsinki, P.O. Box 43, FI-00014 Helsinki, Finland"},{"name":"Algorithmiq Ltd, Kanavakatu 3C 00160 Helsinki, Finland"}]}],"member":"219","published-online":{"date-parts":[[2023,7,20]]},"reference":[{"volume-title":"The theory of open quantum systems","year":"2002","author":"Breuer H.-P.","key":"S1230161223500099BIB001"},{"key":"S1230161223500099BIB002","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-23354-8","volume-title":"Open quantum systems. An introduction","author":"Rivas A.","year":"2012"},{"key":"S1230161223500099BIB003","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.physa.2014.02.004","volume":"402","author":"Vidiella-Barranco A.","year":"2014","journal-title":"Phys. A: Stat. Mech. Appl."},{"key":"S1230161223500099BIB004","doi-asserted-by":"crossref","first-page":"1879","DOI":"10.1080\/09500340.2018.1471172","volume":"65","author":"De\u00e7ordi G. L.","year":"2018","journal-title":"J. Mod. 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