{"id":"https://openalex.org/W2921972598","doi":"https://doi.org/10.1137/19m1299529","title":"From the Hartree Equation to the Vlasov--Poisson System: Strong Convergence for a Class of Mixed States","display_name":"From the Hartree Equation to the Vlasov--Poisson System: Strong Convergence for a Class of Mixed States","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2921972598","doi":"https://doi.org/10.1137/19m1299529","mag":"2921972598"},"language":"en","primary_location":{"id":"doi:10.1137/19m1299529","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1299529","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068016048","display_name":"Chiara Saffirio","orcid":"https://orcid.org/0000-0001-7939-6498"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chiara Saffirio","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068016048"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5848,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58041006,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"52","issue":"6","first_page":"5533","last_page":"5553"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9997000098228455,"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/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.9995999932289124,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hartree","display_name":"Hartree","score":0.7854662537574768},{"id":"https://openalex.org/keywords/coulomb","display_name":"Coulomb","score":0.7167069911956787},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6672042012214661},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.5491042137145996},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5141165852546692},{"id":"https://openalex.org/keywords/vlasov-equation","display_name":"Vlasov equation","score":0.5134264230728149},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4920179545879364},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4835755228996277},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.41435861587524414},{"id":"https://openalex.org/keywords/quantum-electrodynamics","display_name":"Quantum electrodynamics","score":0.404363214969635},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.395609974861145},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.29531723260879517},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2341862916946411},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22197329998016357},{"id":"https://openalex.org/keywords/plasma","display_name":"Plasma","score":0.1698056161403656},{"id":"https://openalex.org/keywords/electron","display_name":"Electron","score":0.08268716931343079},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.062295377254486084}],"concepts":[{"id":"https://openalex.org/C145196801","wikidata":"https://www.wikidata.org/wiki/Q476572","display_name":"Hartree","level":2,"score":0.7854662537574768},{"id":"https://openalex.org/C9342510","wikidata":"https://www.wikidata.org/wiki/Q25406","display_name":"Coulomb","level":3,"score":0.7167069911956787},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6672042012214661},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.5491042137145996},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5141165852546692},{"id":"https://openalex.org/C186175660","wikidata":"https://www.wikidata.org/wiki/Q2323892","display_name":"Vlasov equation","level":3,"score":0.5134264230728149},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4920179545879364},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4835755228996277},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.41435861587524414},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.404363214969635},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.395609974861145},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.29531723260879517},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2341862916946411},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22197329998016357},{"id":"https://openalex.org/C82706917","wikidata":"https://www.wikidata.org/wiki/Q10251","display_name":"Plasma","level":2,"score":0.1698056161403656},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.08268716931343079},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.062295377254486084},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/19m1299529","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1299529","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:edoc.unibas.ch:81507","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401836","display_name":"edoc (University of Basel)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1850255","host_organization_name":"University of Basel","host_organization_lineage":["https://openalex.org/I1850255"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Preprint"},{"id":"pmh:oai:arXiv.org:1903.06013","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.06013","pdf_url":"https://arxiv.org/pdf/1903.06013","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"mag:2921972598","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1903.06013","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1903.06013","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1903.06013","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.5451/unibas-ep81507","is_oa":true,"landing_page_url":"https://doi.org/10.5451/unibas-ep81507","pdf_url":null,"source":{"id":"https://openalex.org/S4306401836","display_name":"edoc (University of Basel)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1850255","host_organization_name":"University of Basel","host_organization_lineage":["https://openalex.org/I1850255"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:edoc.unibas.ch:81507","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401836","display_name":"edoc (University of Basel)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1850255","host_organization_name":"University of Basel","host_organization_lineage":["https://openalex.org/I1850255"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1201993172","display_name":null,"funder_award_id":"PCEFP2 181153","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4430097687","display_name":null,"funder_award_id":"PZ00P2","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4985866398","display_name":null,"funder_award_id":"PCEFP2_181153","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G518571780","display_name":"Rhetorische Ironie in den direkten Reden der Ilias.","funder_award_id":"61287","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5683934959","display_name":null,"funder_award_id":"Eccellenza","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G6153190716","display_name":"Derivation of the Boltzmann equation from classical and quantum dynamics","funder_award_id":"161287","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G6691483310","display_name":null,"funder_award_id":"Ambizione","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G7963649488","display_name":"From Newton and Schr\u00f6dinger many-body dynamics to the Boltzmann equation","funder_award_id":"181153","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G8383338716","display_name":null,"funder_award_id":"PZ00P2_161287/1","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W14417158","https://openalex.org/W1605580234","https://openalex.org/W1624700874","https://openalex.org/W1963956563","https://openalex.org/W1964164841","https://openalex.org/W1982774977","https://openalex.org/W1990333117","https://openalex.org/W1990499542","https://openalex.org/W1995080413","https://openalex.org/W2000627338","https://openalex.org/W2033289485","https://openalex.org/W2044785095","https://openalex.org/W2052379907","https://openalex.org/W2061532286","https://openalex.org/W2068005474","https://openalex.org/W2081907035","https://openalex.org/W2083916485","https://openalex.org/W2092410600","https://openalex.org/W2115888969","https://openalex.org/W2170455972","https://openalex.org/W2224751643","https://openalex.org/W2316366013","https://openalex.org/W2467924074","https://openalex.org/W2514902007","https://openalex.org/W2580977923","https://openalex.org/W2592378367","https://openalex.org/W2605672426","https://openalex.org/W2769428211","https://openalex.org/W2810019251","https://openalex.org/W2913944535","https://openalex.org/W2921533321","https://openalex.org/W2962895170","https://openalex.org/W2963001965","https://openalex.org/W2963308831","https://openalex.org/W2963453361","https://openalex.org/W2963568002","https://openalex.org/W2963721420","https://openalex.org/W3100539250","https://openalex.org/W3101028886","https://openalex.org/W3101790108","https://openalex.org/W3101833153","https://openalex.org/W3102365483","https://openalex.org/W3103039789","https://openalex.org/W3103072912","https://openalex.org/W3103447571","https://openalex.org/W3104125079","https://openalex.org/W3104439247","https://openalex.org/W3105816599","https://openalex.org/W3161960068","https://openalex.org/W4299135034"],"related_works":["https://openalex.org/W3100111135","https://openalex.org/W1605580234","https://openalex.org/W3100539250","https://openalex.org/W3010367533","https://openalex.org/W3198042276","https://openalex.org/W2917473395","https://openalex.org/W2963001965","https://openalex.org/W3157047185","https://openalex.org/W2976177463","https://openalex.org/W2783852403","https://openalex.org/W2059345730","https://openalex.org/W3085288819","https://openalex.org/W2002757450","https://openalex.org/W1558142966","https://openalex.org/W3102102041","https://openalex.org/W3137228762","https://openalex.org/W165153693","https://openalex.org/W3100523084","https://openalex.org/W2949550165"],"abstract_inverted_index":{"We":[0,19,39],"study":[1],"the":[2,6,16,33,36],"semiclassical":[3],"limit":[4],"from":[5],"time-dependent":[7],"Hartree":[8],"equation":[9],"with":[10],"Coulomb":[11],"or":[12],"gravitational":[13],"potential":[14],"to":[15],"Vlasov--Poisson":[17,37],"equation.":[18,38],"prove":[20],"convergence":[21],"in":[22],"trace":[23],"norm":[24],"for":[25],"mixed":[26,45],"states":[27,47],"under":[28],"a":[29,41],"technical":[30],"assumption":[31],"on":[32],"solution":[34],"of":[35,44],"exhibit":[40],"special":[42],"class":[43],"quasi-free":[46],"which":[48],"satisfy":[49],"this":[50],"assumption.":[51]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
