{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T03:02:36Z","timestamp":1783479756898,"version":"3.55.0"},"reference-count":89,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T00:00:00Z","timestamp":1672704000000},"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 report the step-by-step construction of the exact, closed and explicit expression for the evolution operator U(t) of a localized and isolated qubit in an arbitrary time-dependent field, which for concreteness we assume to be a magnetic field. Our approach is based on the existence of two independent dynamical invariants that enter the expression of SU(2) by means of two strictly related time-dependent, real or complex, parameters. The usefulness of our approach is demonstrated by exactly solving the quantum dynamics of a qubit subject to a controllable time-dependent field that can be realized in the laboratory. We further discuss possible applications to any SU(2) model, as well as the applicability of our method to realistic physical scenarios with different symmetry properties.<\/jats:p>","DOI":"10.3390\/e25010096","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T05:02:30Z","timestamp":1672808550000},"page":"96","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Invariant-Parameterized Exact Evolution Operator for SU(2) Systems with Time-Dependent Hamiltonian"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5257-7309","authenticated-orcid":false,"given":"Hiromichi","family":"Nakazato","sequence":"first","affiliation":[{"name":"Department of Physics, Waseda University, Tokyo 169-8555, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3954-0445","authenticated-orcid":false,"given":"Alessandro","family":"Sergi","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Universit\u00e0 degli Studi di Messina, Viale F. Stagno d\u2019Alcontres 31, 98166 Messina, Italy"},{"name":"Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7780-2296","authenticated-orcid":false,"given":"Agostino","family":"Migliore","sequence":"additional","affiliation":[{"name":"Department of Chemical Sciences, University di Padova, Via Francesco Marzolo, 1, 35131 Padova, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3367-0129","authenticated-orcid":false,"given":"Antonino","family":"Messina","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica ed Informatica dell\u2019Universit\u00e0 di Palermo, Via Archirafi 34, 90123 Palermo, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"023081","DOI":"10.1103\/PhysRevResearch.2.023081","article-title":"Dynamics of quantum systems driven by time-varying Hamiltonians: Solution for the Bloch-Siegert Hamiltonian and applications to NMR","volume":"2","author":"Giscard","year":"2020","journal-title":"Phys. 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