{"id":"https://openalex.org/W2115652279","doi":"https://doi.org/10.1112/jlms/jdu068","title":"Equidistribution of phase shifts in semiclassical potential scattering","display_name":"Equidistribution of phase shifts in semiclassical potential scattering","publication_year":2015,"publication_date":"2015-01-16","ids":{"openalex":"https://openalex.org/W2115652279","doi":"https://doi.org/10.1112/jlms/jdu068","mag":"2115652279"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdu068","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu068","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1311.2353","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jesse Gell-Redman","orcid":null},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jesse Gell-Redman","raw_affiliation_strings":["Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Andrew Hassell","orcid":null},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I2802631561","display_name":"Australian Mathematical Sciences Institute","ror":"https://ror.org/00yn60108","country_code":"AU","type":"other","lineage":["https://openalex.org/I2802631561"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Andrew Hassell","raw_affiliation_strings":["Mathematical Sciences Institute, Australian National University, Canberra 0200, Australia, [email protected]","Mathematical Sciences Institute, Australian National University, Canberra 0200, Australia, andrew.hassell@anu.edu.au"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Sciences Institute, Australian National University, Canberra 0200, Australia, [email protected]","institution_ids":["https://openalex.org/I118347636","https://openalex.org/I2802631561"]},{"raw_affiliation_string":"Mathematical Sciences Institute, Australian National University, Canberra 0200, Australia, andrew.hassell@anu.edu.au","institution_ids":["https://openalex.org/I118347636","https://openalex.org/I2802631561"]}]},{"author_position":"last","author":{"id":null,"display_name":"Steve Zelditch","orcid":null},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]},{"id":"https://openalex.org/I4210100400","display_name":"Northwestern University","ror":"https://ror.org/00m6w7z96","country_code":"PH","type":"education","lineage":["https://openalex.org/I4210100400"]}],"countries":["PH","US"],"is_corresponding":false,"raw_author_name":"Steve Zelditch","raw_affiliation_strings":["Department of Mathematics, Northwestern University, Evanston, IL 60201, USA, [email protected]","Department of Mathematics, Northwestern University, Evanston, IL 60201, USA, zelditch@math.northwestern.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Northwestern University, Evanston, IL 60201, USA, [email protected]","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Department of Mathematics, Northwestern University, Evanston, IL 60201, USA, zelditch@math.northwestern.edu","institution_ids":["https://openalex.org/I111979921","https://openalex.org/I4210100400"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I145311948"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":0.4787,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6221168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"91","issue":"1","first_page":"159","last_page":"179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9251999855041504,"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":0.9251999855041504,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.02280000038444996,"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/T12351","display_name":"Geometry and complex manifolds","score":0.006200000178068876,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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-physics","display_name":"Semiclassical physics","score":0.8464000225067139},{"id":"https://openalex.org/keywords/unit-circle","display_name":"Unit circle","score":0.8238000273704529},{"id":"https://openalex.org/keywords/equidistributed-sequence","display_name":"Equidistributed sequence","score":0.7221999764442444},{"id":"https://openalex.org/keywords/unitarity","display_name":"Unitarity","score":0.6651999950408936},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6577000021934509},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4823000133037567},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.48010000586509705},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.46939998865127563},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.3774000108242035}],"concepts":[{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.8464000225067139},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.8238000273704529},{"id":"https://openalex.org/C50742451","wikidata":"https://www.wikidata.org/wiki/Q1530388","display_name":"Equidistributed sequence","level":2,"score":0.7221999764442444},{"id":"https://openalex.org/C130295795","wikidata":"https://www.wikidata.org/wiki/Q3550684","display_name":"Unitarity","level":2,"score":0.6651999950408936},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6577000021934509},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5285000205039978},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4823000133037567},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.48010000586509705},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.46939998865127563},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.46939998865127563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46639999747276306},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3847000002861023},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.3774000108242035},{"id":"https://openalex.org/C2776333733","wikidata":"https://www.wikidata.org/wiki/Q3045336","display_name":"Fredholm determinant","level":2,"score":0.3506999909877777},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3467000126838684},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3458999991416931},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.3100000023841858},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C161094330","wikidata":"https://www.wikidata.org/wiki/Q581505","display_name":"S-matrix","level":3,"score":0.304500013589859},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.30329999327659607},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C55649039","wikidata":"https://www.wikidata.org/wiki/Q902618","display_name":"Floquet theory","level":3,"score":0.2793999910354614},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C67105901","wikidata":"https://www.wikidata.org/wiki/Q903737","display_name":"Scattering theory","level":3,"score":0.2752000093460083},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.2651999890804291},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1112/jlms/jdu068","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu068","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1311.2353","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.2353","pdf_url":"https://arxiv.org/pdf/1311.2353","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,"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":"pmh:oai:openresearch-repository.anu.edu.au:1885/66394","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/66394","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"Journal article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1311.2353","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.2353","pdf_url":"https://arxiv.org/pdf/1311.2353","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,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1498458032","https://openalex.org/W1576484142","https://openalex.org/W1974479153","https://openalex.org/W1975497098","https://openalex.org/W1979025219","https://openalex.org/W1986981284","https://openalex.org/W1989071770","https://openalex.org/W1994562320","https://openalex.org/W2009766219","https://openalex.org/W2023639168","https://openalex.org/W2026881344","https://openalex.org/W2029770333","https://openalex.org/W2037416698","https://openalex.org/W2046511500","https://openalex.org/W2048065008","https://openalex.org/W2051692245","https://openalex.org/W2053898254","https://openalex.org/W2055040433","https://openalex.org/W2058514105","https://openalex.org/W2060232157","https://openalex.org/W2060752160","https://openalex.org/W2062394371","https://openalex.org/W2064170222","https://openalex.org/W2064812758","https://openalex.org/W2067789018","https://openalex.org/W2067922999","https://openalex.org/W2070141139","https://openalex.org/W2075989556","https://openalex.org/W2078542058","https://openalex.org/W2084403660","https://openalex.org/W2093581683","https://openalex.org/W2505262635","https://openalex.org/W4231706539","https://openalex.org/W4252398182","https://openalex.org/W6631830706","https://openalex.org/W6640641487","https://openalex.org/W6650873232","https://openalex.org/W6676919632"],"related_works":[],"abstract_inverted_index":{"Consider":[0],"the":[1,7,32,35,42,48,57,68,71,77,82],"Hamiltonian":[2],"H:=h2\u2062\u0394+V\u2013E":[3],"where":[4],"\u0394":[5],"is":[6,13,20,26],"positive":[8],"Laplacian":[9],"on":[10,41,56,76],"Rd,":[11],"V\u2208C0\u221e\u2061(Rd)":[12],"a":[14,27],"smooth,":[15],"compactly":[16],"supported":[17],"potential,":[18],"E>0":[19],"an":[21,53],"energy":[22],"level,":[23],"and":[24],"h>0":[25],"semiclassical":[28],"parameter.":[29],"We":[30],"study":[31],"eigenvalues":[33,72],"of":[34,50],"scattering":[36],"matrix":[37],"Sh\u2061(E),":[38],"which":[39],"lie":[40],"unit":[43,78],"circle":[44,79],"S1\u2282C":[45],"due":[46],"to":[47,62],"unitarity":[49],"Sh\u2061(E).":[51],"Under":[52],"appropriate":[54],"hypothesis":[55],"classical":[58],"dynamical":[59],"flow":[60],"corresponding":[61],"H,":[63],"we":[64],"show":[65],"that":[66],"in":[67],"limit":[69],"h\u21920,":[70],"are":[73],"asymptotically":[74],"equidistributed":[75],"away":[80],"from":[81],"point":[83],"1\u2208S1.":[84]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2016-06-24T00:00:00"}
