{"id":"https://openalex.org/W7171362501","doi":"https://doi.org/10.48550/arxiv.2607.22490","title":"The semiclassical limit from Hartree to Vlasov at positive density: strong uniform-in-time convergence and scattering","display_name":"The semiclassical limit from Hartree to Vlasov at positive density: strong uniform-in-time convergence and scattering","publication_year":2026,"publication_date":"2026-07-24","ids":{"openalex":"https://openalex.org/W7171362501","doi":"https://doi.org/10.48550/arxiv.2607.22490"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2607.22490","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.22490","pdf_url":"https://arxiv.org/pdf/2607.22490","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/2607.22490","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5143733360","display_name":"Marnie Smith","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Smith, Marnie","raw_affiliation_strings":["Department of Pure Mathematics and Mathematical Statistics , University of Cambridge"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics , University of Cambridge","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5143733360"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.8095999956130981,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.8095999956130981,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.17640000581741333,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.003100000089034438,"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/semiclassical-limit","display_name":"semiclassical limit","score":0.9950000047683716},{"id":"https://openalex.org/keywords/hartree-equation","display_name":"Hartree equation","score":0.9980000257492065},{"id":"https://openalex.org/keywords/vlasov-equation","display_name":"Vlasov equation","score":0.9829999804496765},{"id":"https://openalex.org/keywords/positive-density","display_name":"positive density","score":0.7039999961853027},{"id":"https://openalex.org/keywords/homogeneous-steady-state","display_name":"homogeneous steady state","score":0.8989999890327454},{"id":"https://openalex.org/keywords/scattering","display_name":"scattering","score":0.5720000267028809},{"id":"https://openalex.org/keywords/global-existence","display_name":"global existence","score":0.8050000071525574},{"id":"https://openalex.org/keywords/phase-mixing","display_name":"phase mixing","score":0.6480000019073486},{"id":"https://openalex.org/keywords/wigner-transform","display_name":"Wigner transform","score":0.9729999899864197},{"id":"https://openalex.org/keywords/weighted-sobolev-spaces","display_name":"weighted Sobolev spaces","score":0.765999972820282}],"concepts":[{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.9153000116348267},{"id":"https://openalex.org/C145196801","wikidata":"https://www.wikidata.org/wiki/Q476572","display_name":"Hartree","level":2,"score":0.6693000197410583},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.5940999984741211},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5863000154495239},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5537999868392944},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.541700005531311},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5275999903678894},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.4821999967098236},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.44119998812675476},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4221999943256378},{"id":"https://openalex.org/C186175660","wikidata":"https://www.wikidata.org/wiki/Q2323892","display_name":"Vlasov equation","level":3,"score":0.40709999203681946},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.39739999175071716},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.387800008058548},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3799000084400177},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.36970001459121704},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.3686000108718872},{"id":"https://openalex.org/C67105901","wikidata":"https://www.wikidata.org/wiki/Q903737","display_name":"Scattering theory","level":3,"score":0.34880000352859497},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.33739998936653137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32190001010894775},{"id":"https://openalex.org/C53702628","wikidata":"https://www.wikidata.org/wiki/Q3090317","display_name":"Classical limit","level":3,"score":0.27970001101493835}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2607.22490","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.22490","pdf_url":"https://arxiv.org/pdf/2607.22490","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.2607.22490","doi":"https://doi.org/10.48550/arxiv.2607.22490","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.22490","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2607.22490","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.22490","pdf_url":"https://arxiv.org/pdf/2607.22490","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":[{"id":"https://openalex.org/G2286686988","display_name":"SLMath: Opening Doors to Mathematics","funder_award_id":"2424139","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4713160749","display_name":null,"funder_award_id":"2424139","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7171362501.pdf","grobid_xml":"https://content.openalex.org/works/W7171362501.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W636566490","https://openalex.org/W1605580234","https://openalex.org/W2064611479","https://openalex.org/W2090496967","https://openalex.org/W2101644050","https://openalex.org/W2108302866","https://openalex.org/W2139794644","https://openalex.org/W2338516057","https://openalex.org/W2900278971","https://openalex.org/W2963892693","https://openalex.org/W2980394875","https://openalex.org/W3043776402","https://openalex.org/W4362696230","https://openalex.org/W4381885041","https://openalex.org/W4389673761","https://openalex.org/W4402706153","https://openalex.org/W4405634790","https://openalex.org/W4411509396","https://openalex.org/W4415098354","https://openalex.org/W4415309515","https://openalex.org/W4416065613","https://openalex.org/W7155166677"],"related_works":["https://openalex.org/W2917473395","https://openalex.org/W3007366270","https://openalex.org/W2963308831","https://openalex.org/W4415309515","https://openalex.org/W3010367533","https://openalex.org/W2980394875","https://openalex.org/W4381885041","https://openalex.org/W2921533321","https://openalex.org/W2921972598","https://openalex.org/W4378977917"],"abstract_inverted_index":{"Strong":[0],"semiclassical":[1,70,82],"convergence":[2,32,83],"from":[3],"the":[4,8,55,64,69,73,81,90,94,100,105],"Hartree":[5,56],"equation":[6,10,57],"to":[7,99],"Vlasov":[9,66],"is":[11,38,84],"established":[12],"in":[13,34],"three":[14],"dimensions":[15],"near":[16],"Penrose-stable":[17],"homogeneous":[18],"steady":[19],"states":[20],"at":[21,104],"positive":[22],"density.":[23],"For":[24],"sufficiently":[25],"regular":[26],"integrable":[27],"interaction":[28],"kernels,":[29],"an":[30],"$O(\\hbar^2)$":[31],"rate":[33,107],"weighted":[35],"Sobolev":[36],"spaces":[37],"proved":[39],"on":[40],"finite":[41],"time":[42],"intervals.":[43],"Combining":[44],"this":[45],"estimate":[46],"with":[47],"earlier":[48],"uniform-in-$\\hbar$":[49],"phase-mixing":[50],"and":[51,61,75,89],"scattering":[52,62,96,102],"bounds":[53],"for":[54,63,86],"yields":[58],"global":[59],"existence":[60],"corresponding":[65],"solution":[67],"through":[68],"limit.":[71],"If":[72],"quantum":[74,95],"classical":[76,101],"initial":[77],"perturbations":[78],"are":[79],"aligned,":[80],"uniform":[85],"all":[87],"times,":[88],"Wigner":[91],"transforms":[92],"of":[93],"profiles":[97],"converge":[98],"profile":[103],"explicit":[106],"$O((\\ln\\hbar^{-1})^{-1/3})$.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-07-28T00:00:00"}