{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T12:33:23Z","timestamp":1754483603170,"version":"3.41.2"},"reference-count":29,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:p> The evolution of mixed states of a closed quantum system is described by a group of evolution superoperators whose infinitesimal generator (the quantum Liouville superoperator, or Liouvillian) determines the mixed-state counterpart of the Schr\u00f6dinger equation: the Liouville\u2013von Neumann equation. When the state space of the system is infinite-dimensional, the Liouville superoperator is unbounded whenever the corresponding Hamiltonian is. In this paper, we provide a rigorous, pedagogically-oriented, and self-contained introduction to the quantum Liouville formalism in the presence of unbounded operators. We present and discuss a characterization of the domain of the Liouville superoperator originally due to M. Courbage; starting from that, we develop some simpler characterizations of the domain of the Liouvillian and its square. We also provide, with explicit proofs, some domains of essential selfadjointness (cores) of the Liouvillian. <\/jats:p>","DOI":"10.1142\/s1230161224500185","type":"journal-article","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T01:43:48Z","timestamp":1735609428000},"source":"Crossref","is-referenced-by-count":2,"title":["On the Liouville\u2013von Neumann Equation for Unbounded Hamiltonians"],"prefix":"10.1142","volume":"31","author":[{"given":"Davide","family":"Lonigro","sequence":"first","affiliation":[{"name":"Department Physik, Friedrich-Alexander-Universit\u00e4t, Erlangen-N\u00fcrnberg, Staudtstra\u00dfe 7, 91058 Erlangen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Hahn","sequence":"additional","affiliation":[{"name":"School of Mathematical and Physical Sciences, Macquarie University, Balaclava Rd, Macquarie Park NSW 2109, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Burgarth","sequence":"additional","affiliation":[{"name":"Department Physik, Friedrich-Alexander-Universit\u00e4t, Erlangen-N\u00fcrnberg, Staudtstra\u00dfe 7, 91058 Erlangen, Germany"},{"name":"School of Mathematical and Physical Sciences, Macquarie University, Balaclava Rd, Macquarie Park NSW 2109, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,12,30]]},"reference":[{"key":"S1230161224500185BIB001","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6404\/ab9fdd"},{"key":"S1230161224500185BIB002","doi-asserted-by":"publisher","DOI":"10.1063\/1.1664868"},{"key":"S1230161224500185BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4371(75)90124-7"},{"key":"S1230161224500185BIB004","doi-asserted-by":"publisher","DOI":"10.1063\/1.522782"},{"key":"S1230161224500185BIB005","doi-asserted-by":"publisher","DOI":"10.1063\/1.1666095"},{"key":"S1230161224500185BIB006","doi-asserted-by":"publisher","DOI":"10.1063\/1.1666422"},{"key":"S1230161224500185BIB007","first-page":"113","volume":"30","author":"Prugove\u010dki E.","year":"1975","journal-title":"Compos. 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