{"id":"https://openalex.org/W3098218983","doi":"https://doi.org/10.3390/e23081073","title":"Isospectral Twirling and Quantum Chaos","display_name":"Isospectral Twirling and Quantum Chaos","publication_year":2021,"publication_date":"2021-08-19","ids":{"openalex":"https://openalex.org/W3098218983","doi":"https://doi.org/10.3390/e23081073","mag":"3098218983","pmid":"https://pubmed.ncbi.nlm.nih.gov/34441214"},"language":"en","primary_location":{"id":"doi:10.3390/e23081073","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23081073","pdf_url":"https://www.mdpi.com/1099-4300/23/8/1073/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/8/1073/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076046686","display_name":"Lorenzo Leone","orcid":"https://orcid.org/0000-0002-0334-7419"},"institutions":[{"id":"https://openalex.org/I33434090","display_name":"University of Massachusetts Boston","ror":"https://ror.org/04ydmy275","country_code":"US","type":"education","lineage":["https://openalex.org/I33434090"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Lorenzo Leone","raw_affiliation_strings":["Physics Department, University of Massachusetts Boston, Boston, MA 02125, USA"],"raw_orcid":"https://orcid.org/0000-0002-0334-7419","affiliations":[{"raw_affiliation_string":"Physics Department, University of Massachusetts Boston, Boston, MA 02125, USA","institution_ids":["https://openalex.org/I33434090"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034539197","display_name":"Salvatore F. E. Oliviero","orcid":"https://orcid.org/0000-0003-3569-085X"},"institutions":[{"id":"https://openalex.org/I33434090","display_name":"University of Massachusetts Boston","ror":"https://ror.org/04ydmy275","country_code":"US","type":"education","lineage":["https://openalex.org/I33434090"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Salvatore F. E. Oliviero","raw_affiliation_strings":["Physics Department, University of Massachusetts Boston, Boston, MA 02125, USA"],"raw_orcid":"https://orcid.org/0000-0003-3569-085X","affiliations":[{"raw_affiliation_string":"Physics Department, University of Massachusetts Boston, Boston, MA 02125, USA","institution_ids":["https://openalex.org/I33434090"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024893268","display_name":"Alioscia Hamma","orcid":"https://orcid.org/0000-0003-0662-719X"},"institutions":[{"id":"https://openalex.org/I33434090","display_name":"University of Massachusetts Boston","ror":"https://ror.org/04ydmy275","country_code":"US","type":"education","lineage":["https://openalex.org/I33434090"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alioscia Hamma","raw_affiliation_strings":["Physics Department, University of Massachusetts Boston, Boston, MA 02125, USA"],"raw_orcid":"https://orcid.org/0000-0003-0662-719X","affiliations":[{"raw_affiliation_string":"Physics Department, University of Massachusetts Boston, Boston, MA 02125, USA","institution_ids":["https://openalex.org/I33434090"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5076046686"],"corresponding_institution_ids":["https://openalex.org/I33434090"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":4.9372,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.95803005,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"23","issue":"8","first_page":"1073","last_page":"1073"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.9998999834060669,"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/T11804","display_name":"Quantum many-body systems","score":0.9998999834060669,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9980999827384949,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/quantum-chaos","display_name":"Quantum chaos","score":0.8035266399383545},{"id":"https://openalex.org/keywords/isospectral","display_name":"Isospectral","score":0.714472770690918},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.6090635061264038},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4900397062301636},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.4522651731967926},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4433947205543518},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.427068829536438},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.414532870054245},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38524457812309265},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.37686294317245483},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3349258601665497},{"id":"https://openalex.org/keywords/quantum-dynamics","display_name":"Quantum dynamics","score":0.25008541345596313}],"concepts":[{"id":"https://openalex.org/C136269434","wikidata":"https://www.wikidata.org/wiki/Q1502341","display_name":"Quantum chaos","level":4,"score":0.8035266399383545},{"id":"https://openalex.org/C2779710842","wikidata":"https://www.wikidata.org/wiki/Q6086323","display_name":"Isospectral","level":2,"score":0.714472770690918},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.6090635061264038},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4900397062301636},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4522651731967926},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4433947205543518},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.427068829536438},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.414532870054245},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38524457812309265},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.37686294317245483},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3349258601665497},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.25008541345596313},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e23081073","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23081073","pdf_url":"https://www.mdpi.com/1099-4300/23/8/1073/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:34441214","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34441214","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:arXiv.org:2011.06011","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.06011","pdf_url":"https://arxiv.org/pdf/2011.06011","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:ca7d76465e794549879313c22a9c6798","is_oa":true,"landing_page_url":"https://doaj.org/article/ca7d76465e794549879313c22a9c6798","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 23, Iss 8, p 1073 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/8/1073/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23081073","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 23; Issue 8; Pages: 1073","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8392229","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8392229","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e23081073","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23081073","pdf_url":"https://www.mdpi.com/1099-4300/23/8/1073/pdf","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3567291050","display_name":null,"funder_award_id":"2014000","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"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3098218983.pdf"},"referenced_works_count":105,"referenced_works":["https://openalex.org/W602904462","https://openalex.org/W1497530417","https://openalex.org/W1571204621","https://openalex.org/W1575867504","https://openalex.org/W1636149824","https://openalex.org/W1677099425","https://openalex.org/W1744159570","https://openalex.org/W1772811847","https://openalex.org/W1826324575","https://openalex.org/W1983850647","https://openalex.org/W1986168108","https://openalex.org/W1994243572","https://openalex.org/W2000281602","https://openalex.org/W2000628151","https://openalex.org/W2004057278","https://openalex.org/W2005309611","https://openalex.org/W2028385846","https://openalex.org/W2034251480","https://openalex.org/W2040689906","https://openalex.org/W2059045419","https://openalex.org/W2070375169","https://openalex.org/W2077599442","https://openalex.org/W2083665622","https://openalex.org/W2085208370","https://openalex.org/W2086818467","https://openalex.org/W2089668319","https://openalex.org/W2094810855","https://openalex.org/W2116102644","https://openalex.org/W2118301480","https://openalex.org/W2129872856","https://openalex.org/W2137001571","https://openalex.org/W2217109888","https://openalex.org/W2247548592","https://openalex.org/W2282168229","https://openalex.org/W2305331350","https://openalex.org/W2339039078","https://openalex.org/W2508304031","https://openalex.org/W2537703961","https://openalex.org/W2550203619","https://openalex.org/W2562886563","https://openalex.org/W2619619341","https://openalex.org/W2619816662","https://openalex.org/W2620407091","https://openalex.org/W2678159642","https://openalex.org/W2688070744","https://openalex.org/W2755803912","https://openalex.org/W2782099770","https://openalex.org/W2790807257","https://openalex.org/W2793632407","https://openalex.org/W2798745388","https://openalex.org/W2798950466","https://openalex.org/W2799267168","https://openalex.org/W2801064005","https://openalex.org/W2804172638","https://openalex.org/W2808166932","https://openalex.org/W2847031378","https://openalex.org/W2886389292","https://openalex.org/W2890911513","https://openalex.org/W2921746574","https://openalex.org/W2948374647","https://openalex.org/W2950872758","https://openalex.org/W2969548060","https://openalex.org/W2972256504","https://openalex.org/W2981274508","https://openalex.org/W2990329149","https://openalex.org/W3005283491","https://openalex.org/W3021887649","https://openalex.org/W3038973560","https://openalex.org/W3043744123","https://openalex.org/W3045190418","https://openalex.org/W3047261995","https://openalex.org/W3077829270","https://openalex.org/W3083575336","https://openalex.org/W3097639094","https://openalex.org/W3098156575","https://openalex.org/W3098218983","https://openalex.org/W3098880662","https://openalex.org/W3099536950","https://openalex.org/W3099651446","https://openalex.org/W3100037049","https://openalex.org/W3100755341","https://openalex.org/W3101135901","https://openalex.org/W3101241776","https://openalex.org/W3101545261","https://openalex.org/W3103198988","https://openalex.org/W3104288617","https://openalex.org/W3104665600","https://openalex.org/W3105534226","https://openalex.org/W3106051480","https://openalex.org/W3112352587","https://openalex.org/W3112980360","https://openalex.org/W3119964110","https://openalex.org/W3121590353","https://openalex.org/W3131268544","https://openalex.org/W3131645664","https://openalex.org/W3139324907","https://openalex.org/W3158211506","https://openalex.org/W3173044126","https://openalex.org/W3195552818","https://openalex.org/W4230630710","https://openalex.org/W4293262148","https://openalex.org/W6636888758","https://openalex.org/W6738655238","https://openalex.org/W6770293945","https://openalex.org/W6789202166"],"related_works":["https://openalex.org/W2064381386","https://openalex.org/W2063161885","https://openalex.org/W601725153","https://openalex.org/W2934566931","https://openalex.org/W4288376261","https://openalex.org/W3098456114","https://openalex.org/W2088733890","https://openalex.org/W1764319771","https://openalex.org/W3111946569","https://openalex.org/W2013202722"],"abstract_inverted_index":{"We":[0,41,85],"show":[1,42,86,151,173],"that":[2,43,87,174],"the":[3,25,29,33,52,59,70,77,80,83,125,155,182,197,203,211],"most":[4],"important":[5],"measures":[6,45,176],"of":[7,28,36,54,58,79,106,161,177,186],"quantum":[8,64,100,165,178,189],"chaos,":[9],"such":[10,44],"as":[11],"frame":[12],"potentials,":[13],"scrambling,":[14],"Loschmidt":[15],"echo":[16],"and":[17,72,99,164,210],"out-of-time-order":[18],"correlators":[19],"(OTOCs),":[20],"can":[21,46,93],"be":[22,49],"described":[23],"by":[24,196,207],"unified":[26],"framework":[27],"isospectral":[30,60,104],"twirling,":[31],"namely":[32],"Haar":[34,126],"average":[35],"a":[37,152,159],"k-fold":[38],"unitary":[39],"channel.":[40],"then":[47],"always":[48],"cast":[50],"in":[51,154],"form":[53],"an":[55,129],"expectation":[56],"value":[57],"twirling.":[61],"In":[62],"literature,":[63],"chaos":[65,179,190],"is":[66],"investigated":[67],"sometimes":[68],"through":[69,76],"spectrum":[71],"some":[73],"other":[74],"times":[75],"eigenvectors":[78,121],"Hamiltonian":[81],"generating":[82],"dynamics.":[84],"thanks":[88],"to":[89,137,188,192],"this":[90],"technique,":[91],"we":[92,150,172],"interpolate":[94],"smoothly":[95],"between":[96,158],"integrable":[97,162,204],"Hamiltonians":[98,107,119,146],"chaotic":[101,115,193],"Hamiltonians.":[102],"The":[103],"twirling":[105],"with":[108,133,141,147],"eigenvector":[109],"stabilizer":[110],"states":[111],"does":[112],"not":[113],"possess":[114],"features,":[116],"unlike":[117],"those":[118],"whose":[120],"are":[122],"taken":[123],"from":[124,202],"measure.":[127],"As":[128],"example,":[130],"OTOCs":[131],"obtained":[132],"Clifford":[134],"resources":[135],"decay":[136],"higher":[138],"values":[139],"compared":[140],"universal":[142],"resources.":[143],"By":[144],"doping":[145],"non-Clifford":[148],"resources,":[149],"crossover":[153],"OTOC":[156],"behavior":[157,185],"class":[160],"models":[163],"chaos.":[166],"Moreover,":[167],"exploiting":[168],"random":[169],"matrix":[170],"theory,":[171],"these":[175],"clearly":[180],"distinguish":[181],"finite":[183],"time":[184],"probes":[187],"corresponding":[191],"spectra":[194,205],"given":[195,206],"Gaussian":[198,212],"Unitary":[199],"Ensemble":[200,214],"(GUE)":[201],"Poisson":[208],"distribution":[209],"Diagonal":[213],"(GDE).":[215]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":9}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
