{"id":"https://openalex.org/W7214225930","doi":"https://doi.org/10.48550/arxiv.2609.28302","title":"Improved convergence radius of the Fer expansion for Hermitian generators","display_name":"Improved convergence radius of the Fer expansion for Hermitian generators","publication_year":2026,"publication_date":"2026-09-23","ids":{"openalex":"https://openalex.org/W7214225930","doi":"https://doi.org/10.48550/arxiv.2609.28302"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.28302","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28302","pdf_url":"https://arxiv.org/pdf/2609.28302","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/2609.28302","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5116271823","display_name":"Lorenzo Bagnasacco","orcid":"https://orcid.org/0009-0000-8001-1751","observed_orcids":["https://orcid.org/0009-0000-8001-1751"]},"institutions":[{"id":"https://openalex.org/I157210198","display_name":"Scuola Normale Superiore","ror":"https://ror.org/03aydme10","country_code":"IT","type":"education","lineage":["https://openalex.org/I157210198"]},{"id":"https://openalex.org/I4210108356","display_name":"National Enterprise for NanoScience and NanoTechnology","ror":"https://ror.org/01sgfhb12","country_code":"IT","type":"facility","lineage":["https://openalex.org/I157210198","https://openalex.org/I162290304","https://openalex.org/I30771326","https://openalex.org/I4210087815","https://openalex.org/I4210108356","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Bagnasacco, Lorenzo","raw_affiliation_strings":["NEST and Scuola Normale Superiore , Piazza dei Cavalieri 7 , I-56126 Pisa , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NEST and Scuola Normale Superiore , Piazza dei Cavalieri 7 , I-56126 Pisa , Italy","institution_ids":["https://openalex.org/I157210198","https://openalex.org/I4210108356"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025356866","display_name":"Vittorio Giovannetti","orcid":"https://orcid.org/0000-0002-7636-9002","observed_orcids":["https://orcid.org/0000-0002-7636-9002"]},"institutions":[{"id":"https://openalex.org/I157210198","display_name":"Scuola Normale Superiore","ror":"https://ror.org/03aydme10","country_code":"IT","type":"education","lineage":["https://openalex.org/I157210198"]},{"id":"https://openalex.org/I4210087815","display_name":"Istituto Nanoscienze","ror":"https://ror.org/0042e5975","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210087815","https://openalex.org/I4210155236"]},{"id":"https://openalex.org/I4210108356","display_name":"National Enterprise for NanoScience and NanoTechnology","ror":"https://ror.org/01sgfhb12","country_code":"IT","type":"facility","lineage":["https://openalex.org/I157210198","https://openalex.org/I162290304","https://openalex.org/I30771326","https://openalex.org/I4210087815","https://openalex.org/I4210108356","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giovannetti, Vittorio","raw_affiliation_strings":["NEST , Scuola Normale Superiore and Istituto Nanoscienze-CNR , Piazza dei Cavalieri 7 , I-56126 Pisa , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NEST , Scuola Normale Superiore and Istituto Nanoscienze-CNR , Piazza dei Cavalieri 7 , I-56126 Pisa , Italy","institution_ids":["https://openalex.org/I157210198","https://openalex.org/I4210087815","https://openalex.org/I4210108356"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.7109000086784363,"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"}},"topics":[{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.7109000086784363,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.17270000278949738,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.04529999941587448,"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/dyson-series","display_name":"Dyson series","score":0.8019999861717224},{"id":"https://openalex.org/keywords/radius-of-convergence","display_name":"radius of convergence","score":0.8479999899864197},{"id":"https://openalex.org/keywords/time-dependent-hamiltonian","display_name":"time-dependent Hamiltonian","score":0.8709999918937683},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"matrix exponential","score":0.8320000171661377}],"concepts":[{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.8586000204086304},{"id":"https://openalex.org/C104416048","wikidata":"https://www.wikidata.org/wiki/Q302518","display_name":"Propagator","level":2,"score":0.7985000014305115},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7128000259399414},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7117999792098999},{"id":"https://openalex.org/C155568369","wikidata":"https://www.wikidata.org/wiki/Q1428097","display_name":"Radius of convergence","level":3,"score":0.5960999727249146},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5782999992370605},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.5651000142097473},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4677000045776367},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.46619999408721924},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.4537000060081482},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3774000108242035},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.36390000581741333},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3587999939918518},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C153363305","wikidata":"https://www.wikidata.org/wiki/Q1306887","display_name":"Geometric series","level":3,"score":0.33899998664855957},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3330000042915344},{"id":"https://openalex.org/C84122041","wikidata":"https://www.wikidata.org/wiki/Q332465","display_name":"Absolute convergence","level":3,"score":0.3280999958515167},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.28369998931884766},{"id":"https://openalex.org/C138888516","wikidata":"https://www.wikidata.org/wiki/Q2266843","display_name":"Infinite product","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.257099986076355},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C76835800","wikidata":"https://www.wikidata.org/wiki/Q859102","display_name":"Cauchy's convergence test","level":5,"score":0.2531000077724457},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.28302","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28302","pdf_url":"https://arxiv.org/pdf/2609.28302","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.2609.28302","doi":"https://doi.org/10.48550/arxiv.2609.28302","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.28302","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.28302","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28302","pdf_url":"https://arxiv.org/pdf/2609.28302","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214225930.pdf","grobid_xml":"https://content.openalex.org/works/W7214225930.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7223130727","https://openalex.org/W1979234802","https://openalex.org/W2073358972","https://openalex.org/W2022547747","https://openalex.org/W4389650543","https://openalex.org/W4388566304","https://openalex.org/W2057919320","https://openalex.org/W2267972227","https://openalex.org/W2023037777","https://openalex.org/W2078290038"],"abstract_inverted_index":{"The":[0,23,95],"Dyson":[1],"series":[2],"expands":[3],"the":[4,13,27,48,61,65,68,77],"propagator":[5,29],"of":[6,12,34,38,50,64,67],"a":[7,58,108],"time-dependent":[8],"Hamiltonian":[9,69],"in":[10,19],"powers":[11],"Hamiltonian,":[14],"but":[15],"its":[16,42],"truncations":[17],"are":[18,103],"general":[20],"not":[21],"unitary.":[22],"Fer":[24],"expansion":[25],"writes":[26],"same":[28],"as":[30],"an":[31],"infinite":[32],"product":[33],"matrix":[35],"exponentials,":[36],"each":[37],"them":[39],"unitary,":[40],"and":[41],"remainder":[43],"decays":[44],"doubly":[45],"exponentially":[46],"with":[47,105],"number":[49],"factors.":[51],"Convergence,":[52],"however,":[53],"is":[54,76],"guaranteed":[55],"only":[56],"within":[57],"finite":[59],"radius:":[60],"time":[62],"integral":[63],"norm":[66],"must":[70],"be":[71],"smaller":[72],"than":[73],"$2$.":[74],"This":[75],"best":[78],"value":[79],"known":[80],"to":[81,92,107],"date.":[82],"Here":[83],"we":[84],"improve":[85],"it":[86,91],"by":[87],"about":[88,93],"$30\\%$,":[89],"raising":[90],"$2.6058$.":[94],"result":[96],"also":[97],"holds":[98],"for":[99],"non-Hermitian":[100],"Hamiltonians":[101],"that":[102],"Hermitian":[104],"respect":[106],"fixed":[109],"metric.":[110]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-25T00:00:00"}