{"id":"https://openalex.org/W7212012291","doi":"https://doi.org/10.48550/arxiv.2609.08257","title":"Asymptotics of Ground States for Helium-Like and Bosonic Atoms in a Two-Cluster Region","display_name":"Asymptotics of Ground States for Helium-Like and Bosonic Atoms in a Two-Cluster Region","publication_year":2026,"publication_date":"2026-09-08","ids":{"openalex":"https://openalex.org/W7212012291","doi":"https://doi.org/10.48550/arxiv.2609.08257"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.08257","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08257","pdf_url":"https://arxiv.org/pdf/2609.08257","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/2609.08257","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003787837","display_name":"Yukimi Goto","orcid":"https://orcid.org/0000-0001-8567-8918","observed_orcids":["https://orcid.org/0000-0001-8567-8918"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Goto, Yukimi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5003787837"],"corresponding_institution_ids":[],"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9771000146865845,"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":0.9771000146865845,"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/T10523","display_name":"Atomic and Molecular Physics","score":0.00800000037997961,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0034000000450760126,"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/ground-state","display_name":"ground state","score":0.8569999933242798},{"id":"https://openalex.org/keywords/helium-like-atoms","display_name":"helium-like atoms","score":0.8140000104904175},{"id":"https://openalex.org/keywords/bosonic-atoms","display_name":"bosonic atoms","score":0.9419999718666077},{"id":"https://openalex.org/keywords/asymptotic-behavior","display_name":"asymptotic behavior","score":0.8299999833106995},{"id":"https://openalex.org/keywords/one-particle-density","display_name":"one-particle density","score":0.9580000042915344},{"id":"https://openalex.org/keywords/threshold-behavior","display_name":"threshold behavior","score":0.5220000147819519},{"id":"https://openalex.org/keywords/essential-spectrum","display_name":"essential spectrum","score":0.6499999761581421},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.4729999899864197}],"concepts":[{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.8051999807357788},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6689000129699707},{"id":"https://openalex.org/C9342510","wikidata":"https://www.wikidata.org/wiki/Q25406","display_name":"Coulomb","level":3,"score":0.5564000010490417},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.53329998254776},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5109000205993652},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4681999981403351},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4341999888420105},{"id":"https://openalex.org/C174084160","wikidata":"https://www.wikidata.org/wiki/Q908049","display_name":"Bound state","level":2,"score":0.4083000123500824},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.383899986743927},{"id":"https://openalex.org/C53964469","wikidata":"https://www.wikidata.org/wiki/Q230895","display_name":"Density of states","level":2,"score":0.32249999046325684},{"id":"https://openalex.org/C4839761","wikidata":"https://www.wikidata.org/wiki/Q212111","display_name":"Spectral line","level":2,"score":0.29989999532699585},{"id":"https://openalex.org/C184779094","wikidata":"https://www.wikidata.org/wiki/Q26383","display_name":"Atomic physics","level":1,"score":0.2985000014305115},{"id":"https://openalex.org/C80845027","wikidata":"https://www.wikidata.org/wiki/Q15144062","display_name":"Continuous spectrum","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.2937000095844269},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.26499998569488525}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.08257","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08257","pdf_url":"https://arxiv.org/pdf/2609.08257","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.2609.08257","doi":"https://doi.org/10.48550/arxiv.2609.08257","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.08257","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:2609.08257","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08257","pdf_url":"https://arxiv.org/pdf/2609.08257","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/G3614000447","display_name":"\u9023\u7d9a\u7a7a\u9593\u4e0a\u306e\u591a\u4f53\u554f\u984c\u3068\u683c\u5b50\u5834\u306e\u7406\u8ad6\u306e\u6570\u5b66\u89e3\u6790","funder_award_id":"26K16996","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212012291.pdf","grobid_xml":"https://content.openalex.org/works/W7212012291.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2045697456","https://openalex.org/W2007041818","https://openalex.org/W1989555326","https://openalex.org/W127031872","https://openalex.org/W2029590184","https://openalex.org/W1994787428","https://openalex.org/W1637810997","https://openalex.org/W2086142687","https://openalex.org/W1652923970","https://openalex.org/W2950584511"],"abstract_inverted_index":{"We":[0,63],"study":[1],"the":[2,19,46,51,56,70,79],"asymptotic":[3],"behavior":[4],"of":[5,9],"positive":[6],"ground":[7,21,30],"states":[8],"$N$-particle":[10,20],"atomic":[11],"Coulomb":[12],"Hamiltonians":[13],"in":[14,45],"a":[15],"two-cluster":[16],"region.":[17],"For":[18],"state":[22,31],"$\u03c8$,":[23],"its":[24],"one-particle":[25],"density":[26],"$\u03c1$,":[27],"and":[28,82],"$(N-1)$-particle":[29],"$\u03d5$,":[32],"we":[33],"show":[34],"that":[35],"for":[36],"$0<\u03b1<1$,":[37],"as":[38],"$|x_N|\\to\\infty$,":[39],"$\u03c8(x_1,\\dots,x_N)/\\sqrt{\u03c1(x_N)}=":[40],"\u03d5(x_1,\\dots,x_{N-1})+O(|x_N|^{-2+\u03b1}":[41],"\\ln":[42],"|x_N|)$":[43],"uniformly":[44],"region":[47,52],"$|x_i|\\le":[48,53],"|x_N|^\u03b1$.":[49],"In":[50],"R_0\\ln":[54],"|x_N|$,":[55],"convergence":[57],"rate":[58],"is":[59],"$O(|x_N|^{-2}":[60],"(\\ln":[61],"|x_N|)^2)$.":[62],"also":[64],"establish":[65],"an":[66],"$O(|x_N|^{-2})$":[67],"bound":[68],"on":[69],"squared":[71],"$L^2$":[72],"error.":[73],"These":[74],"results":[75],"hold":[76],"both":[77],"below":[78],"essential":[80],"spectrum":[81],"at":[83],"threshold.":[84]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-10T00:00:00"}