{"id":"https://openalex.org/W7220665306","doi":"https://doi.org/10.48550/arxiv.2610.04170","title":"Exact Finite-Channel Schur Moments of the Wigner-Smith Matrix with a Tunnel Barrier","display_name":"Exact Finite-Channel Schur Moments of the Wigner-Smith Matrix with a Tunnel Barrier","publication_year":2026,"publication_date":"2026-10-03","ids":{"openalex":"https://openalex.org/W7220665306","doi":"https://doi.org/10.48550/arxiv.2610.04170"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.04170","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04170","pdf_url":"https://arxiv.org/pdf/2610.04170","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/2610.04170","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051401475","display_name":"Israel F. Araujo","orcid":"https://orcid.org/0000-0002-0308-8701","observed_orcids":["https://orcid.org/0000-0002-0308-8701"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Araujo, Israel F.","raw_affiliation_strings":["data cybernetics ssc GmbH , Landsberg am Lech , 86899 , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"data cybernetics ssc GmbH , Landsberg am Lech , 86899 , Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5051401475"],"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9955999851226807,"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":0.9955999851226807,"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/T11716","display_name":"Random Matrices and Applications","score":0.002199999988079071,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.0005000000237487257,"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/tunnel-barrier","display_name":"tunnel barrier","score":0.7829999923706055},{"id":"https://openalex.org/keywords/chaotic-cavities","display_name":"chaotic cavities","score":0.7599999904632568},{"id":"https://openalex.org/keywords/time-reversal-symmetry-breaking","display_name":"time-reversal symmetry breaking","score":0.8889999985694885},{"id":"https://openalex.org/keywords/circular-unitary-ensemble","display_name":"circular unitary ensemble","score":0.7879999876022339},{"id":"https://openalex.org/keywords/toeplitz-determinants","display_name":"Toeplitz determinants","score":0.777999997138977},{"id":"https://openalex.org/keywords/schur-polynomials","display_name":"Schur functions","score":0.7409999966621399},{"id":"https://openalex.org/keywords/semiclassical-expansion","display_name":"semiclassical expansion","score":0.7950000166893005},{"id":"https://openalex.org/keywords/open-quantum-systems","display_name":"open quantum systems","score":0.4230000078678131}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8260999917984009},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.6241999864578247},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6118000149726868},{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.5843999981880188},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.53329998254776},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.522599995136261},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.5095999836921692},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.46540001034736633},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4153999984264374},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.39070001244544983},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.375900000333786},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3659000098705292},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.36309999227523804},{"id":"https://openalex.org/C4285052","wikidata":"https://www.wikidata.org/wiki/Q3406268","display_name":"Moment problem","level":3,"score":0.3398999869823456},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C194571181","wikidata":"https://www.wikidata.org/wiki/Q7449306","display_name":"Semi-infinite","level":2,"score":0.32429999113082886},{"id":"https://openalex.org/C133978748","wikidata":"https://www.wikidata.org/wiki/Q15955882","display_name":"Reflection symmetry","level":2,"score":0.3208000063896179},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.3163999915122986},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.2971999943256378},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28279998898506165},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.04170","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04170","pdf_url":"https://arxiv.org/pdf/2610.04170","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.2610.04170","doi":"https://doi.org/10.48550/arxiv.2610.04170","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.04170","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.04170","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04170","pdf_url":"https://arxiv.org/pdf/2610.04170","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/W7220665306.pdf","grobid_xml":"https://content.openalex.org/works/W7220665306.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1571128870","https://openalex.org/W1838463878","https://openalex.org/W1966657448","https://openalex.org/W1989131438","https://openalex.org/W1994358979","https://openalex.org/W2014764702","https://openalex.org/W2029293171","https://openalex.org/W2034307084","https://openalex.org/W2077439650","https://openalex.org/W2080015688","https://openalex.org/W2085777776","https://openalex.org/W2108866307","https://openalex.org/W2134984950","https://openalex.org/W2798362366","https://openalex.org/W2979694964","https://openalex.org/W4283814431","https://openalex.org/W4386459149","https://openalex.org/W7214492247"],"related_works":["https://openalex.org/W2798362366","https://openalex.org/W1886472961","https://openalex.org/W2966092508","https://openalex.org/W2971628959","https://openalex.org/W1993034118","https://openalex.org/W3006816932","https://openalex.org/W3100355571","https://openalex.org/W1982915213","https://openalex.org/W4386459149","https://openalex.org/W7221133609"],"abstract_inverted_index":{"We":[0,58,204],"consider":[1],"the":[2,40,43,65,96,107,111,123,144,159,179,186,191,201,224,235,248,255],"Wigner--Smith":[3,67,251],"time-delay":[4,258],"matrix":[5,45,68],"of":[6,18,27,42,64,87,114],"a":[7,14,23,76,81,88,99,103,129,155],"chaotic":[8],"cavity":[9],"with":[10,102,247],"broken":[11],"time-reversal":[12],"symmetry,":[13],"finite":[15,140,209],"number":[16],"$M$":[17],"equivalent":[19],"open":[20],"channels,":[21],"and":[22,75,137,162,215,253,260],"uniform":[24],"tunnel":[25],"barrier":[26,77,108,135],"reflection":[28],"probability":[29],"$R$.":[30],"Exact":[31],"random-matrix":[32,193],"results":[33],"for":[34,51,133,195,211,220],"nonideal":[35,66,250],"coupling":[36],"are":[37,54,241],"known":[38,192],"at":[39],"level":[41],"joint":[44],"distribution,":[46],"whereas":[47],"explicit":[48],"finite-channel":[49,257],"formulas":[50,259],"Schur":[52,62,89,221],"moments":[53,142],"much":[55],"less":[56],"developed.":[57],"show":[59],"that":[60,197],"every":[61,173],"moment":[63],"factorizes":[69],"into":[70,154],"its":[71],"ideal-coupling":[72],"inverse-Laguerre":[73],"value":[74],"factor":[78],"given":[79],"by":[80],"circular":[82],"unitary":[83],"ensemble":[84],"(CUE)":[85],"average":[86],"polynomial.":[90],"A":[91],"dual-Cauchy":[92],"generating":[93,131],"function":[94,132],"reduces":[95],"latter":[97],"to":[98,158,167,172,262],"Toeplitz":[100],"determinant":[101],"rational":[104],"symbol,":[105],"placing":[106],"problem":[109],"within":[110],"classical":[112],"theory":[113],"exact":[115,124,150,208,217,249],"CUE":[116,125,237],"characteristic-polynomial":[117],"ratios.":[118],"For":[119,178],"one-row":[120],"partitions,":[121],"specializing":[122],"ratio":[126,151,238],"formula":[127,152],"gives":[128],"closed":[130],"all":[134,139,212],"coefficients":[136],"therefore":[138,231],"delay-time":[141],"in":[143,176,190,234,244],"allowed":[145],"range":[146],"$n\\le":[147],"M$.":[148],"The":[149,228],"decomposes":[153],"sector":[156],"visible":[157],"semiclassical":[160,202,263],"expansion":[161],"an":[163,207,216],"additional":[164],"contribution":[165,183,230],"proportional":[166],"$R^{M+1}$,":[168],"which":[169,240],"is":[170,198],"invisible":[171],"algebraic":[174],"order":[175],"$1/M$.":[177],"second":[180],"moment,":[181],"this":[182],"exactly":[184],"reproduces":[185],"exponentially":[187],"small":[188],"term":[189],"expression":[194],"$\\langle\u03c4_W^2\\rangle$":[196],"absent":[199],"from":[200],"expansion.":[203],"also":[205],"derive":[206],"sum":[210],"one-column":[213],"partitions":[214],"complement":[218],"symmetry":[219],"averages":[222],"inside":[223],"$M\\times":[225],"M$":[226],"square.":[227],"new":[229],"lies":[232],"not":[233],"underlying":[236],"identities,":[239],"classical,":[242],"but":[243],"combining":[245],"them":[246],"mapping":[252],"extracting":[254],"resulting":[256],"corrections":[261],"Schur-moment":[264],"conjectures.":[265]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}