{"id":"https://openalex.org/W4405902504","doi":"https://doi.org/10.1142/s1230161224500185","title":"On the Liouville\u2013von Neumann Equation for Unbounded Hamiltonians","display_name":"On the Liouville\u2013von Neumann Equation for Unbounded Hamiltonians","publication_year":2024,"publication_date":"2024-12-01","ids":{"openalex":"https://openalex.org/W4405902504","doi":"https://doi.org/10.1142/s1230161224500185"},"language":"en","primary_location":{"id":"doi:10.1142/s1230161224500185","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1230161224500185","pdf_url":null,"source":{"id":"https://openalex.org/S27332288","display_name":"Open Systems & Information Dynamics","issn_l":"1230-1612","issn":["1230-1612","1573-1324","1793-7191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Systems &amp; Information Dynamics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061461158","display_name":"Davide Lonigro","orcid":"https://orcid.org/0000-0002-0792-8122"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Davide Lonigro","raw_affiliation_strings":["Department Physik, Friedrich-Alexander-Universit\u00e4t, Erlangen-N\u00fcrnberg, Staudtstra\u00dfe 7, 91058 Erlangen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department Physik, Friedrich-Alexander-Universit\u00e4t, Erlangen-N\u00fcrnberg, Staudtstra\u00dfe 7, 91058 Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101872977","display_name":"Alexander Hahn","orcid":"https://orcid.org/0000-0002-4152-9854"},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Alexander Hahn","raw_affiliation_strings":["School of Mathematical and Physical Sciences, Macquarie University, Balaclava Rd, Macquarie Park NSW 2109, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical and Physical Sciences, Macquarie University, Balaclava Rd, Macquarie Park NSW 2109, Australia","institution_ids":["https://openalex.org/I99043593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044459179","display_name":"Daniel Burgarth","orcid":"https://orcid.org/0000-0003-4063-1264"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]},{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU","DE"],"is_corresponding":false,"raw_author_name":"Daniel Burgarth","raw_affiliation_strings":["Department Physik, Friedrich-Alexander-Universit\u00e4t, Erlangen-N\u00fcrnberg, Staudtstra\u00dfe 7, 91058 Erlangen, Germany","School of Mathematical and Physical Sciences, Macquarie University, Balaclava Rd, Macquarie Park NSW 2109, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department Physik, Friedrich-Alexander-Universit\u00e4t, Erlangen-N\u00fcrnberg, Staudtstra\u00dfe 7, 91058 Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"School of Mathematical and Physical Sciences, Macquarie University, Balaclava Rd, Macquarie Park NSW 2109, Australia","institution_ids":["https://openalex.org/I99043593"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061461158"],"corresponding_institution_ids":["https://openalex.org/I181369854"],"apc_list":null,"apc_paid":null,"fwci":4.9615,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.96758801,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"31","issue":"04","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6663426160812378},{"id":"https://openalex.org/keywords/von-neumann-architecture","display_name":"Von Neumann architecture","score":0.5267231464385986},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.5103475451469421},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.49135199189186096},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4497140645980835},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4002353250980377},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.17033082246780396}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6663426160812378},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.5267231464385986},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.5103475451469421},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49135199189186096},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4497140645980835},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4002353250980377},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.17033082246780396}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1230161224500185","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1230161224500185","pdf_url":null,"source":{"id":"https://openalex.org/S27332288","display_name":"Open Systems & Information Dynamics","issn_l":"1230-1612","issn":["1230-1612","1573-1324","1793-7191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Systems &amp; Information Dynamics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W23439300","https://openalex.org/W227029647","https://openalex.org/W1503042153","https://openalex.org/W1973605095","https://openalex.org/W1986119538","https://openalex.org/W1999538080","https://openalex.org/W2013896337","https://openalex.org/W2029707392","https://openalex.org/W2034637037","https://openalex.org/W2042417564","https://openalex.org/W2056271465","https://openalex.org/W2061697884","https://openalex.org/W2071054253","https://openalex.org/W2072663231","https://openalex.org/W2089113045","https://openalex.org/W2124714273","https://openalex.org/W2304061949","https://openalex.org/W2506448866","https://openalex.org/W2728017284","https://openalex.org/W2802008906","https://openalex.org/W2804172638","https://openalex.org/W3013437806","https://openalex.org/W3023894225","https://openalex.org/W3039948875","https://openalex.org/W3041885192","https://openalex.org/W3100711216"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2772186013","https://openalex.org/W3114280011","https://openalex.org/W4287549745","https://openalex.org/W4221167520","https://openalex.org/W1543808017","https://openalex.org/W1988058848","https://openalex.org/W2589216245","https://openalex.org/W2356994189","https://openalex.org/W2081148092"],"abstract_inverted_index":{"The":[0],"evolution":[1,16],"of":[2,5,15,31,43,77,86,89,106,109,123,127],"mixed":[3],"states":[4],"a":[6,13,63,84],"closed":[7],"quantum":[8,22,71],"system":[9,45],"is":[10,46,51],"described":[11],"by":[12],"group":[14],"superoperators":[17],"whose":[18],"infinitesimal":[19],"generator":[20],"(the":[21],"Liouville":[23,49,72,91],"superoperator,":[24],"or":[25],"Liouvillian)":[26],"determines":[27],"the":[28,32,35,40,44,48,54,70,75,87,90,107,110,128],"mixed-state":[29],"counterpart":[30],"Schr\u00f6dinger":[33],"equation:":[34],"Liouville\u2013von":[36],"Neumann":[37],"equation.":[38],"When":[39],"state":[41],"space":[42],"infinite-dimensional,":[47],"superoperator":[50,92],"unbounded":[52,78],"whenever":[53],"corresponding":[55],"Hamiltonian":[56],"is.":[57],"In":[58],"this":[59],"paper,":[60],"we":[61,101],"provide":[62],"rigorous,":[64],"pedagogically-oriented,":[65],"and":[66,82,112],"self-contained":[67],"introduction":[68],"to":[69,95],"formalism":[73],"in":[74],"presence":[76],"operators.":[79],"We":[80,115],"present":[81],"discuss":[83],"characterization":[85],"domain":[88,108],"originally":[93],"due":[94],"M.":[96],"Courbage;":[97],"starting":[98],"from":[99],"that,":[100],"develop":[102],"some":[103,121],"simpler":[104],"characterizations":[105],"Liouvillian":[111],"its":[113],"square.":[114],"also":[116],"provide,":[117],"with":[118],"explicit":[119],"proofs,":[120],"domains":[122],"essential":[124],"selfadjointness":[125],"(cores)":[126],"Liouvillian.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
