{"id":"https://openalex.org/W4387435280","doi":"https://doi.org/10.1088/1742-5468/acf8bd","title":"Is the Moyal equation for the Wigner function a quantum analogue of the Liouville equation?","display_name":"Is the Moyal equation for the Wigner function a quantum analogue of the Liouville equation?","publication_year":2023,"publication_date":"2023-09-01","ids":{"openalex":"https://openalex.org/W4387435280","doi":"https://doi.org/10.1088/1742-5468/acf8bd"},"language":"en","primary_location":{"id":"doi:10.1088/1742-5468/acf8bd","doi":"https://doi.org/10.1088/1742-5468/acf8bd","is_oa":false,"landing_page_url":"https://doi.org/10.1088/1742-5468/acf8bd","pdf_url":null,"source":{"id":"https://openalex.org/S167943036","display_name":"Journal of Statistical Mechanics Theory and Experiment","issn_l":"1742-5468","issn":["1742-5468"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311669","host_organization_name":"Institute of Physics","host_organization_lineage":["https://openalex.org/P4310311669"],"host_organization_lineage_names":["Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Statistical Mechanics: Theory and Experiment","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2307.16316","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069775796","display_name":"E. E. Perepelkin","orcid":"https://orcid.org/0000-0001-5505-4055","observed_orcids":["https://orcid.org/0000-0001-5505-4055"]},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]},{"id":"https://openalex.org/I32699454","display_name":"Joint Institute for Nuclear Research","ror":"https://ror.org/044yd9t77","country_code":"RU","type":"facility","lineage":["https://openalex.org/I32699454"]},{"id":"https://openalex.org/I4210110898","display_name":"Moscow Technical University of Communication and Informatics","ror":"https://ror.org/015zw2f19","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210110898"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"E E Perepelkin","raw_affiliation_strings":["Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia","Joint Institute for Nuclear Research, Moscow region, Dubna 141980, Russia","Moscow Technical University of Communications and Informatics, Moscow 123423, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia","institution_ids":["https://openalex.org/I19880235"]},{"raw_affiliation_string":"Joint Institute for Nuclear Research, Moscow region, Dubna 141980, Russia","institution_ids":["https://openalex.org/I32699454"]},{"raw_affiliation_string":"Moscow Technical University of Communications and Informatics, Moscow 123423, Russia","institution_ids":["https://openalex.org/I4210110898"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081398624","display_name":"\u0411. \u0418. \u0421\u0430\u0434\u043e\u0432\u043d\u0438\u043a\u043e\u0432","orcid":"https://orcid.org/0009-0004-9933-8737","observed_orcids":["https://orcid.org/0009-0004-9933-8737"]},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"B I Sadovnikov","raw_affiliation_strings":["Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia","institution_ids":["https://openalex.org/I19880235"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108632743","display_name":"\u041d\u0430\u0442\u0430\u043b\u044c\u044f \u0413\u0435\u0440\u043c\u0430\u043d\u043e\u0432\u043d\u0430 \u0418\u043d\u043e\u0437\u0435\u043c\u0446\u0435\u0432\u0430","orcid":"https://orcid.org/0009-0001-8222-239X","observed_orcids":["https://orcid.org/0009-0001-8222-239X"]},"institutions":[{"id":"https://openalex.org/I4210094364","display_name":"Dubna State University","ror":"https://ror.org/00smn7825","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210094364"]},{"id":"https://openalex.org/I4210110898","display_name":"Moscow Technical University of Communication and Informatics","ror":"https://ror.org/015zw2f19","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210110898"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"N G Inozemtseva","raw_affiliation_strings":["Dubna State University, Moscow region, Dubna 141980, Russia","Moscow Technical University of Communications and Informatics, Moscow 123423, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dubna State University, Moscow region, Dubna 141980, Russia","institution_ids":["https://openalex.org/I4210094364"]},{"raw_affiliation_string":"Moscow Technical University of Communications and Informatics, Moscow 123423, Russia","institution_ids":["https://openalex.org/I4210110898"]}]},{"author_position":"middle","author":{"id":null,"display_name":"E V Burlakov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210110898","display_name":"Moscow Technical University of Communication and Informatics","ror":"https://ror.org/015zw2f19","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210110898"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"E V Burlakov","raw_affiliation_strings":["Moscow Technical University of Communications and Informatics, Moscow 123423, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Moscow Technical University of Communications and Informatics, Moscow 123423, Russia","institution_ids":["https://openalex.org/I4210110898"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079210697","display_name":"P. V. Afonin","orcid":"https://orcid.org/0009-0008-4532-8671","observed_orcids":["https://orcid.org/0009-0008-4532-8671"]},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"P V Afonin","raw_affiliation_strings":["Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia","institution_ids":["https://openalex.org/I19880235"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5069775796"],"corresponding_institution_ids":["https://openalex.org/I19880235","https://openalex.org/I32699454","https://openalex.org/I4210110898"],"apc_list":{"value":3045,"currency":"USD","value_usd":3045},"apc_paid":null,"fwci":0.9316,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.67758206,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"2023","issue":"9","first_page":"093102","last_page":"093102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.4912000000476837,"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"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.4912000000476837,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.4796999990940094,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.004600000102072954,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/wigner-function","display_name":"Wigner function","score":1.0},{"id":"https://openalex.org/keywords/liouville-equation","display_name":"Liouville equation","score":0.9850000143051147},{"id":"https://openalex.org/keywords/phase-space","display_name":"phase space","score":0.6129999756813049},{"id":"https://openalex.org/keywords/planck-constant","display_name":"Planck constant","score":0.7620000243186951},{"id":"https://openalex.org/keywords/classical-limit","display_name":"classical limit","score":0.6510000228881836},{"id":"https://openalex.org/keywords/quantum-classical-correspondence","display_name":"quantum-classical correspondence","score":0.6589999794960022},{"id":"https://openalex.org/keywords/phase-space-trajectories","display_name":"phase trajectories","score":0.7110000252723694}],"concepts":[{"id":"https://openalex.org/C197111296","wikidata":"https://www.wikidata.org/wiki/Q122894","display_name":"Planck constant","level":3,"score":0.6896600723266602},{"id":"https://openalex.org/C151077058","wikidata":"https://www.wikidata.org/wiki/Q233415","display_name":"Wigner distribution function","level":3,"score":0.6155663728713989},{"id":"https://openalex.org/C99669320","wikidata":"https://www.wikidata.org/wiki/Q6823722","display_name":"Method of quantum characteristics","level":5,"score":0.6136910915374756},{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.6111789345741272},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4829241931438446},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4626755118370056},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.4508020579814911},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.4413908123970032},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.43229275941848755},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.397209107875824},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3718937337398529},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3481088876724243},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.31149888038635254},{"id":"https://openalex.org/C136269434","wikidata":"https://www.wikidata.org/wiki/Q1502341","display_name":"Quantum chaos","level":4,"score":0.2118769884109497},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.18672075867652893},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1088/1742-5468/acf8bd","doi":"https://doi.org/10.1088/1742-5468/acf8bd","is_oa":false,"landing_page_url":"https://doi.org/10.1088/1742-5468/acf8bd","pdf_url":null,"source":{"id":"https://openalex.org/S167943036","display_name":"Journal of Statistical Mechanics Theory and Experiment","issn_l":"1742-5468","issn":["1742-5468"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311669","host_organization_name":"Institute of Physics","host_organization_lineage":["https://openalex.org/P4310311669"],"host_organization_lineage_names":["Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Statistical Mechanics: Theory and Experiment","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2307.16316","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2307.16316","pdf_url":"https://arxiv.org/pdf/2307.16316","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2307.16316","doi":"https://doi.org/10.48550/arxiv.2307.16316","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2307.16316","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2307.16316","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2307.16316","pdf_url":"https://arxiv.org/pdf/2307.16316","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387435280.pdf","grobid_xml":"https://content.openalex.org/works/W4387435280.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1886890904","https://openalex.org/W2024454387","https://openalex.org/W2062712424","https://openalex.org/W2080169805","https://openalex.org/W2101731201","https://openalex.org/W2170649178","https://openalex.org/W2419308095","https://openalex.org/W2587326901","https://openalex.org/W3028072287","https://openalex.org/W3165898261","https://openalex.org/W3190085170","https://openalex.org/W3217467777","https://openalex.org/W4200634093","https://openalex.org/W4233371905","https://openalex.org/W4312192468","https://openalex.org/W4321366953"],"related_works":["https://openalex.org/W3135459036","https://openalex.org/W2952340968","https://openalex.org/W7028885144","https://openalex.org/W4306705599","https://openalex.org/W1546985609","https://openalex.org/W3135791834","https://openalex.org/W1971518213","https://openalex.org/W2078403359","https://openalex.org/W2937613327","https://openalex.org/W2951129125"],"abstract_inverted_index":{"Abstract":[0],"The":[1,19,134],"Moyal":[2,44,82,91,113,206],"equation":[3,24,45,83,92,97,114,176],"describes":[4],"the":[5,8,16,23,35,43,51,59,62,66,69,77,81,90,94,99,108,112,120,127,137,146,151,163,174,180,187,193,198,201,205,213,224,228,239,245],"evolution":[6],"of":[7,11,22,34,42,50,61,80,111,126,165,173,200,204,221,223,230],"Wigner":[9,182],"function":[10,183],"a":[12,47,88,131,155,160,166,231],"quantum":[13,48,140,157],"system":[14,158],"in":[15,162,186,192],"phase":[17,194],"space.":[18],"right-hand":[20,78,202],"side":[21,79,110,203],"contains":[25],"an":[26,40,169,218],"infinite":[27,219],"series":[28,128],"with":[29,159],"coefficients":[30],"proportional":[31],"to":[32,65,73,85,145,150,238],"powers":[33],"Planck":[36,70,121,147],"constant.":[37],"There":[38],"is":[39,142,177,184,209,217,233],"interpretation":[41],"as":[46,68],"analogue":[49],"classical":[52,63,95,138,246],"Liouville":[53,96],"equation.":[54],"Indeed,":[55],"if":[56],"one":[57],"uses":[58],"notion":[60],"passage":[64],"limit":[67],"constant":[71],"tends":[72,84],"zero,":[74],"then":[75],"formally":[76],"zero.":[86],"As":[87],"result,":[89],"becomes":[93],"for":[98],"distribution":[100],"function.":[101],"In":[102],"this":[103],"paper,":[104],"we":[105],"show":[106],"that":[107,211],"right":[109],"does":[115],"not":[116,144],"explicitly":[117],"depend":[118],"on":[119,197,212],"constant,":[122,148],"and":[123,139,179,235],"all":[124,241],"terms":[125],"can":[129],"make":[130],"significant":[132],"contribution.":[133],"transition":[135],"between":[136],"descriptions":[141],"related":[143],"but":[149],"spatial":[152,214],"scale.":[153],"For":[154],"model":[156],"potential":[161],"form":[164],"\u00abquadratic":[167],"funnel\u00bb,":[168],"exact":[170],"3D":[171],"solution":[172],"Schr\u00f6dinger":[175],"found":[178],"corresponding":[181],"constructed":[185],"paper.":[188],"Using":[189],"trajectory":[190,232],"analysis":[191],"space,":[195],"based":[196],"representation":[199],"equation,":[207],"it":[208],"shown":[210],"microscale":[215],"there":[216],"number":[220],"\u00abtrajectories\u00bb":[222,242],"particle":[225],"motion":[226],"(thereby":[227],"concept":[229],"indefinite),":[234],"when":[236],"passing":[237],"macroscale,":[240],"concentrate":[243],"around":[244],"trajectory.":[247]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2023-10-09T00:00:00"}