{"id":"https://openalex.org/W7216074414","doi":"https://doi.org/10.48550/arxiv.2610.02108","title":"Resonance expansions and local-energy decay estimates for Dirac operators","display_name":"Resonance expansions and local-energy decay estimates for Dirac operators","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7216074414","doi":"https://doi.org/10.48550/arxiv.2610.02108"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02108","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02108","pdf_url":"https://arxiv.org/pdf/2610.02108","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/2610.02108","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5154675261","display_name":"Zhuo Chen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Zhuo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5005932281","display_name":"Michael Melgaard","orcid":"https://orcid.org/0000-0003-3595-6953","observed_orcids":["https://orcid.org/0000-0003-3595-6953"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Melgaard, Michael","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":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":0.9976000189781189,"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":0.9976000189781189,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0019000000320374966,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":9.999999747378752e-05,"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/dirac-operator","display_name":"Dirac operator","score":0.9300000071525574},{"id":"https://openalex.org/keywords/semiclassical-operators","display_name":"semiclassical operators","score":0.6290000081062317},{"id":"https://openalex.org/keywords/resonance","display_name":"resonance","score":0.8420000076293945},{"id":"https://openalex.org/keywords/local-energy-decay","display_name":"local energy decay","score":0.878000020980835},{"id":"https://openalex.org/keywords/fbi-transform","display_name":"FBI transform","score":0.4909999966621399},{"id":"https://openalex.org/keywords/escape-function","display_name":"escape function","score":0.7979999780654907},{"id":"https://openalex.org/keywords/propagators","display_name":"propagators","score":0.5619999766349792},{"id":"https://openalex.org/keywords/three-dimensional-operators","display_name":"three-dimensional operators","score":0.3479999899864197}],"concepts":[{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.8463000059127808},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6172000169754028},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6104999780654907},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.574400007724762},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.5683000087738037},{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.5213000178337097},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5174000263214111},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5126000046730042},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.45179998874664307},{"id":"https://openalex.org/C174084160","wikidata":"https://www.wikidata.org/wiki/Q908049","display_name":"Bound state","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.3531000018119812},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.34139999747276306},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.2870999872684479},{"id":"https://openalex.org/C81571819","wikidata":"https://www.wikidata.org/wiki/Q1426722","display_name":"Resolvent formalism","level":4,"score":0.28519999980926514},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.26910001039505005},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2574999928474426},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02108","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02108","pdf_url":"https://arxiv.org/pdf/2610.02108","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.2610.02108","doi":"https://doi.org/10.48550/arxiv.2610.02108","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02108","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.02108","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02108","pdf_url":"https://arxiv.org/pdf/2610.02108","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":[{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7216074414.pdf","grobid_xml":"https://content.openalex.org/works/W7216074414.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7169568261"],"related_works":["https://openalex.org/W7169568261","https://openalex.org/W2973120286","https://openalex.org/W2064770518","https://openalex.org/W2791595301","https://openalex.org/W2793027989","https://openalex.org/W4415024853","https://openalex.org/W2068513622","https://openalex.org/W2032837853","https://openalex.org/W1684806152","https://openalex.org/W7154663651"],"abstract_inverted_index":{"We":[0,99,142],"study":[1],"resonance":[2,35,78],"expansions":[3,79],"and":[4,37,72,137,210],"localised":[5,82],"long-time":[6],"dynamics":[7],"for":[8,80,87,95,132,176,205,216],"three-dimensional":[9],"semiclassical":[10],"Dirac":[11],"operators.":[12],"For":[13],"smooth":[14],"Hermitian":[15],"matrix-valued":[16],"perturbations":[17,104],"which":[18],"are":[19],"analytic":[20],"outside":[21],"a":[22,53,63,73,107,123,129,149,171,196,201,212],"compact":[23],"set,":[24],"we":[25,76,127,169],"first":[26],"obtain":[27,128],"exponential":[28],"cut-off":[29,135],"resolvent":[30,136,209,220],"bounds":[31,39],"away":[32],"from":[33],"the":[34,46,59,112,133,154,158,166,181,186,206,217],"set":[36],"polynomial":[38,130,146],"in":[40,106,117,153],"thin":[41],"resonance-free":[42,114,182],"rectangles":[43],"adjacent":[44],"to":[45,102,200],"real":[47],"axis.":[48],"Combining":[49],"these":[50],"estimates":[51],"with":[52,122,165],"local":[54],"$\\Oc(h^{-3})$":[55],"upper":[56],"bound":[57,131,204],"on":[58],"number":[60],"of":[61,66],"resonances,":[62],"pigeonhole":[64],"selection":[65],"admissible":[67],"contours,":[68],"almost-analytic":[69],"functional":[70],"calculus,":[71],"Cauchy--Green":[74],"deformation,":[75],"derive":[77,185],"spectrally":[81],"propagators.":[83],"Positive-energy":[84],"resonances":[85,93],"contribute":[86,94],"large":[88,96],"positive":[89],"times,":[90],"whereas":[91],"negative-energy":[92],"negative":[97],"times.":[98],"then":[100],"specialise":[101],"mass-type":[103],"$\\mbf\u03b2V(x)$":[105],"nontrapping":[108],"energy":[109],"window.":[110],"Using":[111],"logarithmic":[113,222],"region":[115],"established":[116],"our":[118],"earlier":[119],"work":[120],"together":[121],"quantitative":[124],"FBI-transform/escape-function":[125],"argument,":[126],"continued":[134,219],"deduce":[138],"rapid":[139],"local-energy":[140,188],"decay.":[141],"subsequently":[143],"refine":[144],"this":[145],"estimate":[147,174],"by":[148],"finite-time":[150],"propagation":[151],"argument":[152],"undistorted":[155],"region.":[156],"Introducing":[157],"maximal":[159],"positive-sheet":[160],"connection":[161],"time":[162],"$T_\u03c7$":[163],"associated":[164],"spatial":[167],"cutoff,":[168],"prove":[170],"geometric":[172],"continued-resolvent":[173],"and,":[175],"every":[177],"fixed":[178],"$M$":[179],"below":[180],"depth":[183],"constant,":[184],"explicit":[187],"decay":[189],"threshold":[190],"$T_N>T_\u03c7+(N+1)/M$.":[191],"The":[192],"same":[193],"analysis":[194],"gives":[195],"rigorous":[197],"microlocal":[198],"obstruction":[199],"uniform":[202],"$[h\\log(1/h)]^{-1}$":[203],"full":[207],"distorted":[208],"identifies":[211],"finite-flight-time":[213],"amplification":[214],"mechanism":[215],"sandwiched":[218],"at":[221],"depth.":[223]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}