{"id":"https://openalex.org/W4313330581","doi":"https://doi.org/10.22331/q-2022-12-29-886","title":"Solvable model of deep thermalization with distinct design times","display_name":"Solvable model of deep thermalization with distinct design times","publication_year":2022,"publication_date":"2022-12-29","ids":{"openalex":"https://openalex.org/W4313330581","doi":"https://doi.org/10.22331/q-2022-12-29-886"},"language":"en","primary_location":{"id":"doi:10.22331/q-2022-12-29-886","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-12-29-886","pdf_url":"https://quantum-journal.org/papers/q-2022-12-29-886/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2022-12-29-886/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029987551","display_name":"Matteo Ippoliti","orcid":"https://orcid.org/0000-0003-4095-0038"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matteo Ippoliti","raw_affiliation_strings":["Department of Physics, Stanford University, Stanford, CA 94305, USA"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Stanford University, Stanford, CA 94305, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081677188","display_name":"Wen Wei Ho","orcid":"https://orcid.org/0000-0001-7702-2900"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["SG","US"],"is_corresponding":false,"raw_author_name":"Wen Wei Ho","raw_affiliation_strings":["Department of Physics, National University of Singapore, Singapore 117542","Department of Physics, Stanford University, Stanford, CA 94305, USA"],"affiliations":[{"raw_affiliation_string":"Department of Physics, National University of Singapore, Singapore 117542","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"Department of Physics, Stanford University, Stanford, CA 94305, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029987551"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":8.4029,"has_fulltext":true,"cited_by_count":58,"citation_normalized_percentile":{"value":0.98427457,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"6","issue":null,"first_page":"886","last_page":"886"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":1.0,"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":1.0,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10382","display_name":"Quantum and electron transport phenomena","score":0.9970999956130981,"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/thermalisation","display_name":"Thermalisation","score":0.8166306614875793},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.6675060987472534},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6532456874847412},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.6374415159225464},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.618288516998291},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.5519900321960449},{"id":"https://openalex.org/keywords/quantum-chaos","display_name":"Quantum chaos","score":0.539171576499939},{"id":"https://openalex.org/keywords/imperfect","display_name":"Imperfect","score":0.5198455452919006},{"id":"https://openalex.org/keywords/wave-function","display_name":"Wave function","score":0.4630145728588104},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.4503154754638672},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.42330366373062134},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4166290760040283},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3645082414150238},{"id":"https://openalex.org/keywords/quantum-dynamics","display_name":"Quantum dynamics","score":0.3043113350868225},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18794658780097961},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08640581369400024}],"concepts":[{"id":"https://openalex.org/C15359245","wikidata":"https://www.wikidata.org/wiki/Q1347805","display_name":"Thermalisation","level":2,"score":0.8166306614875793},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.6675060987472534},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6532456874847412},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6374415159225464},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.618288516998291},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.5519900321960449},{"id":"https://openalex.org/C136269434","wikidata":"https://www.wikidata.org/wiki/Q1502341","display_name":"Quantum chaos","level":4,"score":0.539171576499939},{"id":"https://openalex.org/C2780310539","wikidata":"https://www.wikidata.org/wiki/Q12547192","display_name":"Imperfect","level":2,"score":0.5198455452919006},{"id":"https://openalex.org/C113603373","wikidata":"https://www.wikidata.org/wiki/Q2362761","display_name":"Wave function","level":2,"score":0.4630145728588104},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.4503154754638672},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.42330366373062134},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4166290760040283},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3645082414150238},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.3043113350868225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18794658780097961},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08640581369400024},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2022-12-29-886","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-12-29-886","pdf_url":"https://quantum-journal.org/papers/q-2022-12-29-886/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2208.10542","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2208.10542","pdf_url":"https://arxiv.org/pdf/2208.10542","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:be740da415ae46b3b47a8348a8f9ce7a","is_oa":true,"landing_page_url":"https://doaj.org/article/be740da415ae46b3b47a8348a8f9ce7a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 6, p 886 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2022-12-29-886","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-12-29-886","pdf_url":"https://quantum-journal.org/papers/q-2022-12-29-886/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.6200000047683716}],"awards":[{"id":"https://openalex.org/G1625084116","display_name":null,"funder_award_id":"GBMF8686","funder_id":"https://openalex.org/F4320306202","funder_display_name":"Gordon and Betty Moore Foundation"},{"id":"https://openalex.org/G2569156841","display_name":null,"funder_award_id":"A-8000599-00-00","funder_id":"https://openalex.org/F4320320698","funder_display_name":"National University of Singapore"},{"id":"https://openalex.org/G4767620732","display_name":null,"funder_award_id":"A-8000599-01-00","funder_id":"https://openalex.org/F4320320698","funder_display_name":"National University of Singapore"}],"funders":[{"id":"https://openalex.org/F4320306202","display_name":"Gordon and Betty Moore Foundation","ror":"https://ror.org/006wxqw41"},{"id":"https://openalex.org/F4320320698","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49"},{"id":"https://openalex.org/F4320334432","display_name":"Stanford Research Computing Center, Stanford University","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4313330581.pdf","grobid_xml":"https://content.openalex.org/works/W4313330581.grobid-xml"},"referenced_works_count":104,"referenced_works":["https://openalex.org/W1985536767","https://openalex.org/W1986168108","https://openalex.org/W2034251480","https://openalex.org/W2081113208","https://openalex.org/W2086452860","https://openalex.org/W2087210658","https://openalex.org/W2094366212","https://openalex.org/W2116123253","https://openalex.org/W2126511900","https://openalex.org/W2140622323","https://openalex.org/W2170620327","https://openalex.org/W2206331421","https://openalex.org/W2493448115","https://openalex.org/W2512685237","https://openalex.org/W2537703961","https://openalex.org/W2540688686","https://openalex.org/W2566350286","https://openalex.org/W2619816662","https://openalex.org/W2735457220","https://openalex.org/W2766333524","https://openalex.org/W2766492598","https://openalex.org/W2786366947","https://openalex.org/W2791488214","https://openalex.org/W2799031278","https://openalex.org/W2799034832","https://openalex.org/W2807823044","https://openalex.org/W2886483748","https://openalex.org/W2886712022","https://openalex.org/W2904416995","https://openalex.org/W2914454605","https://openalex.org/W2922951482","https://openalex.org/W2926751802","https://openalex.org/W2945488351","https://openalex.org/W2963956175","https://openalex.org/W2982169647","https://openalex.org/W2990695459","https://openalex.org/W2995027688","https://openalex.org/W2997323873","https://openalex.org/W3006255022","https://openalex.org/W3006823398","https://openalex.org/W3009738078","https://openalex.org/W3020745342","https://openalex.org/W3040854059","https://openalex.org/W3043723517","https://openalex.org/W3057824142","https://openalex.org/W3087827914","https://openalex.org/W3097070339","https://openalex.org/W3097824418","https://openalex.org/W3100755341","https://openalex.org/W3102711922","https://openalex.org/W3102911478","https://openalex.org/W3103104453","https://openalex.org/W3103870741","https://openalex.org/W3105358656","https://openalex.org/W3109913413","https://openalex.org/W3112167980","https://openalex.org/W3117345688","https://openalex.org/W3118869143","https://openalex.org/W3121608281","https://openalex.org/W3129405940","https://openalex.org/W3131591276","https://openalex.org/W3134336374","https://openalex.org/W3141069787","https://openalex.org/W3164167509","https://openalex.org/W3165255987","https://openalex.org/W3169221790","https://openalex.org/W3173899054","https://openalex.org/W3179469771","https://openalex.org/W3185682824","https://openalex.org/W3186107346","https://openalex.org/W3201137765","https://openalex.org/W3208869263","https://openalex.org/W3212522598","https://openalex.org/W3212981721","https://openalex.org/W3216251070","https://openalex.org/W3216628913","https://openalex.org/W4200630628","https://openalex.org/W4225659926","https://openalex.org/W4225770019","https://openalex.org/W4226185604","https://openalex.org/W4226300323","https://openalex.org/W4238640560","https://openalex.org/W4281651499","https://openalex.org/W4281688327","https://openalex.org/W4281702142","https://openalex.org/W4282984473","https://openalex.org/W4286007969","https://openalex.org/W4291992583","https://openalex.org/W4293171638","https://openalex.org/W4293583948","https://openalex.org/W4294628716","https://openalex.org/W4295884212","https://openalex.org/W4297815953","https://openalex.org/W4301055545","https://openalex.org/W4308170891","https://openalex.org/W4310576936","https://openalex.org/W4312205426","https://openalex.org/W4318309504","https://openalex.org/W4320878781","https://openalex.org/W4385878897","https://openalex.org/W4389190205","https://openalex.org/W6604850228","https://openalex.org/W6811987182","https://openalex.org/W6820552363"],"related_works":["https://openalex.org/W2550812089","https://openalex.org/W2022750399","https://openalex.org/W1608432621","https://openalex.org/W148356241","https://openalex.org/W400179824","https://openalex.org/W2051057398","https://openalex.org/W3100744940","https://openalex.org/W2056548857","https://openalex.org/W566097453","https://openalex.org/W2035295916"],"abstract_inverted_index":{"We":[0,151],"study":[1],"the":[2,23,26,52,87,103,135,144],"emergence":[3],"over":[4,111],"time":[5,89,113],"of":[6,11,25,39,55,63,99,119,137,146],"a":[7,16,37,120,130],"universal,":[8],"uniform":[9],"distribution":[10],"quantum":[12,42,60],"states":[13],"supported":[14],"on":[15],"finite":[17,121],"subsystem,":[18],"induced":[19],"by":[20],"projectively":[21],"measuring":[22],"rest":[24],"system.":[27],"Dubbed<mml:math":[28],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow":[29],"class=\"MJX-TeXAtom-ORD\"><mml:mtext":[30],"class=\"MJX-tex-mathit\"":[31],"mathvariant=\"italic\">deep":[32],"thermalization</mml:mtext></mml:mrow></mml:math>,":[33],"this":[34,69],"phenomenon":[35,70],"represents":[36],"form":[38],"equilibration":[40],"in":[41,65,80,142],"many-body":[43],"systems":[44],"stronger":[45],"than":[46],"regular":[47,91],"thermalization,":[48],"which":[49],"only":[50],"constrains":[51],"ensemble-averaged":[53],"values":[54],"observables.":[56],"While":[57],"there":[58],"exist":[59],"circuit":[61],"models":[62],"dynamics":[64,101],"one":[66],"dimension":[67],"where":[68,102],"can":[71,106],"be":[72,107],"shown":[73,108],"to":[74,109,124],"arise":[75],"exactly,":[76],"these":[77],"are":[78],"special":[79],"that":[81],"deep":[82],"thermalization":[83,141],"occurs":[84],"at":[85],"precisely":[86],"same":[88],"as":[90],"thermalization.":[92],"Here,":[93],"we":[94],"present":[95],"an":[96,125],"exactly-solvable":[97],"model":[98,116],"chaotic":[100],"two":[104],"processes":[105],"occur":[110],"different":[112],"scales.":[114],"The":[115],"is":[117],"composed":[118],"subsystem":[122],"coupled":[123],"infinite":[126],"random-matrix":[127],"bath":[128],"through":[129],"small":[131],"constriction,":[132],"and":[133,139],"highlights":[134],"role":[136],"locality":[138],"imperfect":[140],"constraining":[143],"formation":[145],"such":[147],"universal":[148],"wavefunction":[149],"distributions.":[150],"test":[152],"our":[153],"analytical":[154],"predictions":[155],"against":[156],"exact":[157],"numerical":[158],"simulations,":[159],"finding":[160],"excellent":[161],"agreement.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":32},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":9}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
