{"id":"https://openalex.org/W2980243199","doi":"https://doi.org/10.1137/18m1222831","title":"Frozen Gaussian Approximation for the Dirac Equation in Semiclassical Regime","display_name":"Frozen Gaussian Approximation for the Dirac Equation in Semiclassical Regime","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2980243199","doi":"https://doi.org/10.1137/18m1222831","mag":"2980243199"},"language":"en","primary_location":{"id":"doi:10.1137/18m1222831","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1222831","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103251601","display_name":"Lihui Chai","orcid":"https://orcid.org/0000-0001-5096-0577"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lihui Chai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078194875","display_name":"Emmanuel Lorin","orcid":"https://orcid.org/0000-0001-8854-4739"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Emmanuel Lorin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004956299","display_name":"Xu Yang","orcid":"https://orcid.org/0000-0001-6239-1922"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu Yang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-6239-1922","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4928,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.61688474,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"57","issue":"5","first_page":"2383","last_page":"2412"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9922000169754028,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9922000169754028,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9919000267982483,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.991100013256073,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semiclassical-physics","display_name":"Semiclassical physics","score":0.9192889928817749},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.7320893406867981},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6997759938240051},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.5966333150863647},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5396443009376526},{"id":"https://openalex.org/keywords/dirac-equation","display_name":"Dirac equation","score":0.5268389582633972},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5094144940376282},{"id":"https://openalex.org/keywords/dirac","display_name":"Dirac (video compression format)","score":0.466740220785141},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4410727024078369},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.26878809928894043},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.2496689260005951},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20605090260505676},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.1479482352733612}],"concepts":[{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.9192889928817749},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.7320893406867981},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6997759938240051},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5966333150863647},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5396443009376526},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.5268389582633972},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5094144940376282},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.466740220785141},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4410727024078369},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.26878809928894043},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2496689260005951},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20605090260505676},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.1479482352733612},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1222831","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1222831","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8126542560","display_name":"Parallel Semiclassical Methods for Seismic Wave Propagation, Inversion, and Data Analysis","funder_award_id":"1818592","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/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1037248778","https://openalex.org/W1490137490","https://openalex.org/W1963558395","https://openalex.org/W1966048890","https://openalex.org/W1972324900","https://openalex.org/W1978147557","https://openalex.org/W1979057135","https://openalex.org/W1982686824","https://openalex.org/W1992958286","https://openalex.org/W2005492032","https://openalex.org/W2009507302","https://openalex.org/W2016878173","https://openalex.org/W2026321310","https://openalex.org/W2052669961","https://openalex.org/W2059763171","https://openalex.org/W2068824512","https://openalex.org/W2075286495","https://openalex.org/W2076724430","https://openalex.org/W2080517557","https://openalex.org/W2086585878","https://openalex.org/W2101962226","https://openalex.org/W2111586604","https://openalex.org/W2122723350","https://openalex.org/W2124382907","https://openalex.org/W2141705394","https://openalex.org/W2294874426","https://openalex.org/W2318376939","https://openalex.org/W2466154587","https://openalex.org/W2504946410","https://openalex.org/W2525670483","https://openalex.org/W2734337775","https://openalex.org/W2769444863","https://openalex.org/W2792868234","https://openalex.org/W2897898410","https://openalex.org/W2964199329","https://openalex.org/W3100405256","https://openalex.org/W3105801596","https://openalex.org/W3123381822"],"related_works":["https://openalex.org/W4287813962","https://openalex.org/W1564485841","https://openalex.org/W4287219806","https://openalex.org/W4244688541","https://openalex.org/W1919901593","https://openalex.org/W2521223844","https://openalex.org/W2951283098","https://openalex.org/W105150783","https://openalex.org/W1612231772","https://openalex.org/W2059025438"],"abstract_inverted_index":{"This":[0],"paper":[1],"focuses":[2],"on":[3],"the":[4,9,15,19,23,42,58,67,71,74,78,81,87,98,104,111,117],"derivation":[5],"and":[6,31,113],"analysis":[7],"of":[8,48,70,80,116],"frozen":[10],"Gaussian":[11],"approximation":[12],"(FGA)":[13],"for":[14,56,73],"Dirac":[16,43,75],"equation":[17,44,76],"in":[18,28,61],"semiclassical":[20,99],"regime.":[21],"Unlike":[22],"strictly":[24],"hyperbolic":[25],"system":[26],"studied":[27],"[J.":[29],"Lu":[30],"X.":[32],"Yang,":[33],"Comm.":[34],"Pure":[35],"Appl.":[36],"Math.,":[37],"65":[38],"(2012),":[39],"pp.":[40],"759--789],":[41],"possesses":[45],"eigenfunction":[46],"spaces":[47],"multiplicity":[49],"two,":[50],"which":[51,84],"demands":[52],"more":[53],"delicate":[54],"expansions":[55],"deriving":[57],"amplitude":[59],"equations":[60],"FGA.":[62],"Moreover,":[63],"we":[64],"prove":[65],"that":[66,86],"nonrelativistic":[68,88],"limit":[69,89],"FGA":[72,79,96],"is":[77,90],"Schr\u00f6dinger":[82],"equation,":[83],"shows":[85],"asymptotically":[91],"preserved":[92],"after":[93],"one":[94],"applies":[95],"as":[97],"approximation.":[100],"Numerical":[101],"experiments":[102],"including":[103],"Klein":[105],"paradox":[106],"are":[107],"presented":[108],"to":[109],"illustrate":[110],"method":[112],"confirm":[114],"part":[115],"analytical":[118],"results.":[119]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}