{"id":"https://openalex.org/W7223207744","doi":"https://doi.org/10.48550/arxiv.2610.28846","title":"Methods for Deriving Nonlinear Kinetic Equations from the Dynamics of Quantum Systems","display_name":"Methods for Deriving Nonlinear Kinetic Equations from the Dynamics of Quantum Systems","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223207744","doi":"https://doi.org/10.48550/arxiv.2610.28846"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.28846","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28846","pdf_url":"https://arxiv.org/pdf/2610.28846","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.28846","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029574626","display_name":"V. I. Gerasimenko","orcid":"https://orcid.org/0000-0003-2577-2237","observed_orcids":["https://orcid.org/0000-0003-2577-2237"]},"institutions":[{"id":"https://openalex.org/I190444043","display_name":"Institute of Mathematics","ror":"https://ror.org/04q3mp532","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I190444043"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"Gerasimenko, V. I.","raw_affiliation_strings":["Institute of Mathematics of the NAS of Ukra\u00efne , 3 , Tereshchenkivs'ka Str. , 01601 , Ky\u00efv-4 , Ukra\u00efne"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics of the NAS of Ukra\u00efne , 3 , Tereshchenkivs'ka Str. , 01601 , Ky\u00efv-4 , Ukra\u00efne","institution_ids":["https://openalex.org/I190444043"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029574626"],"corresponding_institution_ids":["https://openalex.org/I190444043"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.8154000043869019,"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/T11804","display_name":"Quantum many-body systems","score":0.8154000043869019,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.046799998730421066,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.026799999177455902,"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/quantum-kinetic-equation","display_name":"quantum kinetic equation","score":0.9670000076293945},{"id":"https://openalex.org/keywords/nonlinear-kinetic-equations","display_name":"nonlinear kinetic equations","score":0.9399999976158142},{"id":"https://openalex.org/keywords/evolution-equations","display_name":"evolution equations","score":0.671999990940094}],"concepts":[{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5946999788284302},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5568000078201294},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.5264999866485596},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5080999732017517},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.47920000553131104},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.4546999931335449},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.41589999198913574},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36959999799728394},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.3628000020980835},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.3441999852657318},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3434000015258789},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.31520000100135803},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.313400000333786},{"id":"https://openalex.org/C19979193","wikidata":"https://www.wikidata.org/wiki/Q25100325","display_name":"Kinetic theory","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.29919999837875366},{"id":"https://openalex.org/C106553664","wikidata":"https://www.wikidata.org/wiki/Q1156744","display_name":"Time evolution","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C2235679","wikidata":"https://www.wikidata.org/wiki/Q6410797","display_name":"Kinetic scheme","level":3,"score":0.26249998807907104}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.28846","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28846","pdf_url":"https://arxiv.org/pdf/2610.28846","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.28846","doi":"https://doi.org/10.48550/arxiv.2610.28846","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.28846","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.28846","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28846","pdf_url":"https://arxiv.org/pdf/2610.28846","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320184","display_name":"London Mathematical Society","ror":"https://ror.org/01r1e1h27"},{"id":"https://openalex.org/F4320321979","display_name":"University of Surrey","ror":"https://ror.org/00ks66431"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223207744.pdf","grobid_xml":"https://content.openalex.org/works/W7223207744.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W27672074","https://openalex.org/W1537383557","https://openalex.org/W1564236980","https://openalex.org/W1828280030","https://openalex.org/W1833174700","https://openalex.org/W1972265727","https://openalex.org/W1979652737","https://openalex.org/W2009041809","https://openalex.org/W2012134495","https://openalex.org/W2032863264","https://openalex.org/W2051114077","https://openalex.org/W2075168679","https://openalex.org/W2079087026","https://openalex.org/W2397982118","https://openalex.org/W2563143231","https://openalex.org/W3000861485","https://openalex.org/W3015912288","https://openalex.org/W3042562017","https://openalex.org/W3081502418","https://openalex.org/W3101309355","https://openalex.org/W3101632146","https://openalex.org/W3101826959","https://openalex.org/W3102985402","https://openalex.org/W3103567947","https://openalex.org/W3186215567","https://openalex.org/W4232638393","https://openalex.org/W4244841876","https://openalex.org/W4280593273","https://openalex.org/W4283765579","https://openalex.org/W4286208246","https://openalex.org/W4312418367","https://openalex.org/W4385932455","https://openalex.org/W4389768882","https://openalex.org/W4402966102","https://openalex.org/W4406022324","https://openalex.org/W4417087337"],"related_works":["https://openalex.org/W1693685925","https://openalex.org/W2010658909","https://openalex.org/W3101632146","https://openalex.org/W2090704329","https://openalex.org/W2053415108","https://openalex.org/W1564236980","https://openalex.org/W2045672910","https://openalex.org/W7097175596","https://openalex.org/W4402576587","https://openalex.org/W2016843613"],"abstract_inverted_index":{"The":[0,24],"article":[1],"outlines":[2],"key":[3],"topics":[4],"related":[5],"to":[6,13],"deriving":[7,40],"kinetic":[8,35,41,69],"equations":[9,19,42,47],"and,":[10],"in":[11],"general,":[12],"the":[14,17,30,56,59,64,67],"relationship":[15],"between":[16],"evolution":[18,46,60],"governing":[20],"quantum":[21,34,49,68],"many-particle":[22],"systems.":[23],"main":[25],"issues":[26],"being":[27],"considered":[28],"are":[29],"mathematical":[31],"origin":[32],"of":[33,45,58,61,66],"equations,":[36],"novel":[37],"methods":[38],"for":[39,48],"from":[43],"hierarchies":[44],"systems,":[50],"specifically":[51],"focusing":[52],"on":[53],"kinetics":[54],"within":[55],"framework":[57],"observables,":[62],"and":[63],"generalization":[65],"equation":[70],"specified":[71],"by":[72],"non-separable":[73],"initial":[74],"states.":[75]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-23T00:00:00"}