{"id":"https://openalex.org/W7167037952","doi":"https://doi.org/10.48550/arxiv.2607.00335","title":"Rigorous analysis of the time-splitting methods for the semiclassical Dirac equation","display_name":"Rigorous analysis of the time-splitting methods for the semiclassical Dirac equation","publication_year":2026,"publication_date":"2026-07-01","ids":{"openalex":"https://openalex.org/W7167037952","doi":"https://doi.org/10.48550/arxiv.2607.00335"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.00335","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00335","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.00335","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139916211","display_name":"He Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, He","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5132706277","display_name":"Jia Yin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yin, Jia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11416","display_name":"Numerical methods for differential equations","score":0.8291000127792358,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.8291000127792358,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.03350000083446503,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.031300000846385956,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/semiclassical-physics","display_name":"Semiclassical physics","score":0.7522000074386597},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6205999851226807},{"id":"https://openalex.org/keywords/dirac","display_name":"Dirac (video compression format)","score":0.4984000027179718},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43320000171661377},{"id":"https://openalex.org/keywords/dirac-equation","display_name":"Dirac equation","score":0.43140000104904175},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4081000089645386},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.3880000114440918},{"id":"https://openalex.org/keywords/space-time","display_name":"Space time","score":0.359499990940094},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.35670000314712524}],"concepts":[{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.7522000074386597},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6205999851226807},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5142999887466431},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.4984000027179718},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43320000171661377},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.43140000104904175},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4081000089645386},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.39239999651908875},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.3880000114440918},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.375900000333786},{"id":"https://openalex.org/C96402334","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Space time","level":2,"score":0.359499990940094},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.35670000314712524},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.35179999470710754},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3303000032901764},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.3165999948978424},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.31439998745918274},{"id":"https://openalex.org/C103824480","wikidata":"https://www.wikidata.org/wiki/Q185889","display_name":"Time domain","level":2,"score":0.303600013256073},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.287200003862381},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C166126730","wikidata":"https://www.wikidata.org/wiki/Q725309","display_name":"Planck","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C19619285","wikidata":"https://www.wikidata.org/wiki/Q196372","display_name":"Observational error","level":2,"score":0.2590000033378601}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.00335","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00335","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,"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.00335","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00335","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"provide":[1],"rigorous":[2],"error":[3,61,88,108,129,195],"analysis":[4],"of":[5,39,67,122,193],"the":[6,12,22,45,50,56,64,68,72,76,82,86,93,101,106,120,123,136,142,179,191,194],"mass-preserving":[7],"time-splitting":[8,154,182],"methods":[9],"for":[10,92,100,112,131],"solving":[11],"semiclassical":[13],"Dirac":[14],"equation.":[15],"The":[16],"scaled":[17],"Planck":[18],"constant":[19],"$\u03b5$":[20],"in":[21,29,159],"equation":[23],"gives":[24],"rise":[25],"to":[26,119,189],"rapid":[27],"oscillations":[28],"both":[30,113],"space":[31,160],"and":[32,49,81,97,141,161],"time":[33,73,150],"when":[34],"$0<\u03b5\\ll":[35],"1$":[36],"with":[37,147],"wavelengths":[38],"order":[40],"$O(\u03b5)$.":[41],"%We":[42],"prove":[43],"that":[44,171],"first-order":[46,94],"splitting":[47,52,95,103],"$S_1$":[48,96],"second-order":[51,102],"$S_2$":[53],"schemes":[54],"preserve":[55],"total":[57,137],"discretized":[58],"mass.":[59],"Rigorous":[60],"estimates":[62],"reveal":[63],"precise":[65],"dependence":[66],"approximation":[69],"errors":[70],"on":[71],"step":[74],"$\u03c4$,":[75],"spatial":[77,107],"mesh":[78],"size":[79],"$h$,":[80],"parameter":[83],"$\u03b5$.":[84],"Specifically,":[85],"temporal":[87],"scales":[89,109],"as":[90,98,110],"$O\\left(\u03c4/\u03b5^2\\right)$":[91],"$O\\left(\u03c4^2/\u03b5^3\\right)$":[99],"$S_2$,":[104],"while":[105],"$O(h^m/\u03b5^m)$":[111],"methods,":[114,153],"where":[115],"$m$":[116],"is":[117],"related":[118],"regularity":[121],"solution.":[124],"In":[125],"addition,":[126],"we":[127,169],"obtain":[128],"bounds":[130],"key":[132],"physical":[133],"observables,":[134],"including":[135],"probability":[138],"density":[139,144],"$\u03c1$":[140],"current":[143],"$\\mathbf{J}$.":[145],"Compared":[146],"finite":[148],"difference":[149],"domain":[151],"(FDTD)":[152],"approaches":[155],"exhibit":[156],"spectral":[157],"accuracy":[158,173],"retain":[162],"a":[163],"relatively":[164],"low":[165],"computational":[166],"cost.":[167],"Furthermore,":[168],"demonstrate":[170],"higher":[172],"can":[174],"be":[175],"achieved":[176],"by":[177],"employing":[178],"fourth-order":[180],"compact":[181],"($S_\\text{4c}$)":[183],"method.":[184],"Numerical":[185],"experiments":[186],"are":[187],"conducted":[188],"verify":[190],"reliability":[192],"estimates.":[196]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-03T00:00:00"}