{"id":"https://openalex.org/W4415068237","doi":"https://doi.org/10.1103/6mpz-p85s","title":"Free Probability in a Minimal Quantum Circuit Model","display_name":"Free Probability in a Minimal Quantum Circuit Model","publication_year":2026,"publication_date":"2026-05-19","ids":{"openalex":"https://openalex.org/W4415068237","doi":"https://doi.org/10.1103/6mpz-p85s"},"language":"en","primary_location":{"id":"doi:10.1103/6mpz-p85s","doi":"https://doi.org/10.1103/6mpz-p85s","is_oa":true,"landing_page_url":"https://doi.org/10.1103/6mpz-p85s","pdf_url":null,"source":{"id":"https://openalex.org/S137042341","display_name":"Physical Review X","issn_l":"2160-3308","issn":["2160-3308"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-a","jufo-3","ki-jl-2","norway-2","oarl","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review X","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1103/6mpz-p85s","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070997705","display_name":"Felix Fritzsch","orcid":"https://orcid.org/0000-0002-7659-7574","observed_orcids":["https://orcid.org/0000-0002-7659-7574"]},"institutions":[{"id":"https://openalex.org/I4210111875","display_name":"Max Planck Institute for the Physics of Complex Systems","ror":"https://ror.org/01bf9rw71","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210111875"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Felix Fritzsch","raw_affiliation_strings":["Max Planck Institute for the Physics of Complex Systems"],"raw_orcid":"https://orcid.org/0000-0002-7659-7574","affiliations":[{"raw_affiliation_string":"Max Planck Institute for the Physics of Complex Systems","institution_ids":["https://openalex.org/I4210111875"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027939548","display_name":"Pieter W. Claeys","orcid":"https://orcid.org/0000-0001-7150-8459","observed_orcids":["https://orcid.org/0000-0001-7150-8459"]},"institutions":[{"id":"https://openalex.org/I205274468","display_name":"Trinity College Dublin","ror":"https://ror.org/02tyrky19","country_code":"IE","type":"education","lineage":["https://openalex.org/I205274468"]},{"id":"https://openalex.org/I4210111875","display_name":"Max Planck Institute for the Physics of Complex Systems","ror":"https://ror.org/01bf9rw71","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210111875"]}],"countries":["DE","IE"],"is_corresponding":false,"raw_author_name":"Pieter W. Claeys","raw_affiliation_strings":["Max Planck Institute for the Physics of Complex Systems","Trinity College Dublin"],"raw_orcid":"https://orcid.org/0000-0001-7150-8459","affiliations":[{"raw_affiliation_string":"Max Planck Institute for the Physics of Complex Systems","institution_ids":["https://openalex.org/I4210111875"]},{"raw_affiliation_string":"Trinity College Dublin","institution_ids":["https://openalex.org/I205274468"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":4200,"currency":"USD","value_usd":4200},"apc_paid":{"value":4200,"currency":"USD","value_usd":4200},"fwci":8.5912,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.97429806,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"16","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.9990000128746033,"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":0.9990000128746033,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":9.999999747378752e-05,"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/T10622","display_name":"Quantum Mechanics and Applications","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/out-of-time-ordered-correlators","display_name":"out-of-time-order correlators","score":0.9559999704360962},{"id":"https://openalex.org/keywords/free-probability","display_name":"free probability","score":0.7419999837875366},{"id":"https://openalex.org/keywords/free-independence","display_name":"free independence","score":0.578000009059906},{"id":"https://openalex.org/keywords/exponential-decay","display_name":"exponential decay","score":0.5889999866485596},{"id":"https://openalex.org/keywords/influence-matrix","display_name":"influence matrix","score":0.8429999947547913},{"id":"https://openalex.org/keywords/markovian-dynamics","display_name":"Markovian dynamics","score":0.8560000061988831},{"id":"https://openalex.org/keywords/free-cumulants","display_name":"free cumulants","score":0.890999972820282},{"id":"https://openalex.org/keywords/eigenstate-thermalization-hypothesis","display_name":"eigenstate thermalization hypothesis","score":0.9789999723434448},{"id":"https://openalex.org/keywords/quantum-memory","display_name":"quantum memory","score":0.8740000128746033},{"id":"https://openalex.org/keywords/nonequilibrium-dynamics","display_name":"nonequilibrium dynamics","score":0.8410000205039978},{"id":"https://openalex.org/keywords/local-operators","display_name":"local operators","score":0.36899998784065247}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5999000072479248},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5709999799728394},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5145999789237976},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.45989999175071716},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4278999865055084},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.4065999984741211},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.4025000035762787},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.39890000224113464},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.3862000107765198},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.385699987411499},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.382999986410141},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.3418000042438507},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.337799996137619},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.3215000033378601},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C104416048","wikidata":"https://www.wikidata.org/wiki/Q302518","display_name":"Propagator","level":2,"score":0.3158999979496002},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.310699999332428},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.30799999833106995},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.30640000104904175},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.29269999265670776},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.28360000252723694},{"id":"https://openalex.org/C172686274","wikidata":"https://www.wikidata.org/wiki/Q746007","display_name":"Cumulant","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C165973109","wikidata":"https://www.wikidata.org/wiki/Q894014","display_name":"Quantum probability","level":5,"score":0.2824999988079071},{"id":"https://openalex.org/C198377831","wikidata":"https://www.wikidata.org/wiki/Q7269027","display_name":"Quantum correlation","level":5,"score":0.28139999508857727},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.272599995136261},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.2685999870300293},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.26260000467300415},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C70120467","wikidata":"https://www.wikidata.org/wiki/Q515893","display_name":"Free probability","level":2,"score":0.2556000053882599},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.2551000118255615}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1103/6mpz-p85s","doi":"https://doi.org/10.1103/6mpz-p85s","is_oa":true,"landing_page_url":"https://doi.org/10.1103/6mpz-p85s","pdf_url":null,"source":{"id":"https://openalex.org/S137042341","display_name":"Physical Review X","issn_l":"2160-3308","issn":["2160-3308"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-a","jufo-3","ki-jl-2","norway-2","oarl","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review X","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2506.11197","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2506.11197","pdf_url":"https://arxiv.org/pdf/2506.11197","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":"pmh:oai:doaj.org/article:307c4302c8c2485680a0af52124f88c0","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/307c4302c8c2485680a0af52124f88c0","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,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Physical Review X, Vol 16, Iss 3, p 031027 (2026)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2506.11197","doi":"https://doi.org/10.48550/arxiv.2506.11197","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.11197","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":"doi:10.1103/6mpz-p85s","doi":"https://doi.org/10.1103/6mpz-p85s","is_oa":true,"landing_page_url":"https://doi.org/10.1103/6mpz-p85s","pdf_url":null,"source":{"id":"https://openalex.org/S137042341","display_name":"Physical Review X","issn_l":"2160-3308","issn":["2160-3308"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-a","jufo-3","ki-jl-2","norway-2","oarl","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review X","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4412994196","display_name":null,"funder_award_id":"101146632","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4769716545","display_name":null,"funder_award_id":"101146632","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322434","display_name":"Max-Planck-Gesellschaft","ror":"https://ror.org/01hhn8329"},{"id":"https://openalex.org/F4320334322","display_name":"HORIZON EUROPE Framework Programme","ror":null},{"id":"https://openalex.org/F4320338337","display_name":"H2020 Marie Sk\u0142odowska-Curie Actions","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415068237.pdf","grobid_xml":"https://content.openalex.org/works/W4415068237.grobid-xml"},"referenced_works_count":120,"referenced_works":["https://openalex.org/W591099569","https://openalex.org/W1603380880","https://openalex.org/W1826324575","https://openalex.org/W1884490694","https://openalex.org/W1907359947","https://openalex.org/W1919133474","https://openalex.org/W1972912363","https://openalex.org/W1977411678","https://openalex.org/W1985692219","https://openalex.org/W2021115151","https://openalex.org/W2032690805","https://openalex.org/W2051302879","https://openalex.org/W2070375169","https://openalex.org/W2081113208","https://openalex.org/W2087210658","https://openalex.org/W2087543605","https://openalex.org/W2110023503","https://openalex.org/W2118301480","https://openalex.org/W2170068196","https://openalex.org/W2344612405","https://openalex.org/W2537703961","https://openalex.org/W2564126998","https://openalex.org/W2619816662","https://openalex.org/W2620407091","https://openalex.org/W2766333524","https://openalex.org/W2766492598","https://openalex.org/W2776621698","https://openalex.org/W2795330585","https://openalex.org/W2799034832","https://openalex.org/W2802587496","https://openalex.org/W2890911513","https://openalex.org/W2898409026","https://openalex.org/W2903098524","https://openalex.org/W2911592526","https://openalex.org/W2913757230","https://openalex.org/W2922951482","https://openalex.org/W2926751802","https://openalex.org/W2997645441","https://openalex.org/W3009738078","https://openalex.org/W3020815329","https://openalex.org/W3022508877","https://openalex.org/W3034971867","https://openalex.org/W3037042650","https://openalex.org/W3087827914","https://openalex.org/W3114164323","https://openalex.org/W3119795978","https://openalex.org/W3134262554","https://openalex.org/W3135386210","https://openalex.org/W3155896906","https://openalex.org/W3193735523","https://openalex.org/W3201137765","https://openalex.org/W4200630628","https://openalex.org/W4220805243","https://openalex.org/W4226181960","https://openalex.org/W4226343432","https://openalex.org/W4229369371","https://openalex.org/W4238640560","https://openalex.org/W4281688327","https://openalex.org/W4291992583","https://openalex.org/W4293171638","https://openalex.org/W4295004915","https://openalex.org/W4295882732","https://openalex.org/W4298138119","https://openalex.org/W4308435863","https://openalex.org/W4313330581","https://openalex.org/W4313448102","https://openalex.org/W4317242242","https://openalex.org/W4322733479","https://openalex.org/W4360846484","https://openalex.org/W4361001105","https://openalex.org/W4367607216","https://openalex.org/W4377820387","https://openalex.org/W4385878897","https://openalex.org/W4386882828","https://openalex.org/W4386883338","https://openalex.org/W4386935411","https://openalex.org/W4387059916","https://openalex.org/W4387312462","https://openalex.org/W4387526427","https://openalex.org/W4391124227","https://openalex.org/W4391835629","https://openalex.org/W4392098763","https://openalex.org/W4392971707","https://openalex.org/W4396822049","https://openalex.org/W4396978057","https://openalex.org/W4399123829","https://openalex.org/W4400574463","https://openalex.org/W4400884009","https://openalex.org/W4401636231","https://openalex.org/W4401725776","https://openalex.org/W4401994749","https://openalex.org/W4402357419","https://openalex.org/W4402531986","https://openalex.org/W4402705696","https://openalex.org/W4403247135","https://openalex.org/W4403868815","https://openalex.org/W4406693307","https://openalex.org/W4407193266","https://openalex.org/W4407252878","https://openalex.org/W4407407145","https://openalex.org/W4408291087","https://openalex.org/W4408719258","https://openalex.org/W4409013476","https://openalex.org/W4409125804","https://openalex.org/W4409292111","https://openalex.org/W4409528480","https://openalex.org/W4410112205","https://openalex.org/W4411135322","https://openalex.org/W4411330417","https://openalex.org/W4411983890","https://openalex.org/W4415310231","https://openalex.org/W4415403536","https://openalex.org/W4415444424","https://openalex.org/W4415967094","https://openalex.org/W4416524648","https://openalex.org/W4416927794","https://openalex.org/W4417094408","https://openalex.org/W4417200338","https://openalex.org/W4417329526","https://openalex.org/W6968383642"],"related_works":["https://openalex.org/W6968383642","https://openalex.org/W4417063385","https://openalex.org/W4200630628","https://openalex.org/W7214937362","https://openalex.org/W4416259219","https://openalex.org/W6966725389","https://openalex.org/W2906080600","https://openalex.org/W4389555603","https://openalex.org/W2611256894","https://openalex.org/W2785541633"],"abstract_inverted_index":{"Recent":[0],"experimental":[1],"and":[2,62,147,161],"theoretical":[3],"developments":[4],"in":[5,29,93,127,157,170],"many-body":[6],"quantum":[7,35,168],"systems":[8],"motivate":[9],"the":[10,22,40,55,65,81,84,87,105,125,140,148],"study":[11],"of":[12,24,42,58,83,104,111,117,129],"their":[13],"out-of-equilibrium":[14],"properties":[15],"through":[16],"multitime":[17],"correlation":[18],"functions.":[19],"We":[20,53,78],"consider":[21],"dynamics":[23,41,106],"higher-order":[25,60,95,171],"out-of-time-order":[26],"correlators":[27],"(OTOCs)":[28],"a":[30,43,49,94,101,121,163],"minimal":[31],"circuit":[32],"model":[33,38],"for":[34,100,124],"dynamics.":[36],"This":[37,115,145],"mimics":[39],"structured":[44],"subsystem":[45,89],"locally":[46],"coupled":[47],"to":[48,154,166],"maximally":[50],"random":[51],"environment.":[52],"prove":[54],"exponential":[56],"decay":[57],"all":[59],"OTOCs":[61,126],"fully":[63],"characterize":[64],"relevant":[66,149],"timescales,":[67],"showing":[68],"how":[69],"local":[70,88],"operators":[71],"approach":[72,146],"free":[73,130,133],"independence":[74],"at":[75],"late":[76],"times.":[77],"show":[79],"that":[80],"effects":[82],"environment":[85],"on":[86],"can":[90],"be":[91,155],"captured":[92],"influence":[96,150],"matrix,":[97],"which":[98],"allows":[99],"Markovian":[102],"description":[103],"provided":[107],"an":[108],"auxiliary":[109],"degree":[110,116],"freedom":[112,118],"is":[113],"introduced.":[114],"directly":[119],"yields":[120],"dynamical":[122],"picture":[123],"terms":[128],"cumulants":[131],"from":[132,139],"probability,":[134],"consistent":[135],"with":[136],"recent":[137],"predictions":[138],"full":[141],"eigenstate":[142],"thermalization":[143],"hypothesis.":[144],"matrix":[151],"are":[152],"expected":[153],"applicable":[156],"more":[158],"general":[159],"settings":[160],"present":[162],"first":[164],"step":[165],"characterizing":[167],"memory":[169],"OTOCs.":[172]},"counts_by_year":[{"year":2026,"cited_by_count":4}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2025-10-11T00:00:00"}