{"id":"https://openalex.org/W7169558227","doi":"https://doi.org/10.1103/yf98-5fv6","title":"Lyapunov spectrum scaling transition for quasiperiodic nonlinear unitaries","display_name":"Lyapunov spectrum scaling transition for quasiperiodic nonlinear unitaries","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7169558227","doi":"https://doi.org/10.1103/yf98-5fv6"},"language":"en","primary_location":{"id":"doi:10.1103/yf98-5fv6","doi":"https://doi.org/10.1103/yf98-5fv6","is_oa":false,"landing_page_url":"https://doi.org/10.1103/yf98-5fv6","pdf_url":null,"source":{"id":"https://openalex.org/S4210235286","display_name":"Physical review. E","issn_l":"2470-0045","issn":["2470-0045","2470-0053","2470-0061"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2607.14549","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5141097154","display_name":"Xiaodong Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaodong Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105759896","display_name":"Barbara Dietz","orcid":"https://orcid.org/0000-0002-8251-6531","observed_orcids":["https://orcid.org/0000-0002-8251-6531"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Barbara Dietz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5082451237","display_name":"Sergej Flach","orcid":"https://orcid.org/0000-0003-1710-3746","observed_orcids":["https://orcid.org/0000-0003-1710-3746"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sergej Flach","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":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T11804","display_name":"Quantum many-body systems","score":0.2809999883174896,"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":0.2809999883174896,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.21940000355243683,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.21240000426769257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quasiperiodic-potentials","display_name":"quasiperiodic potentials","score":0.9729999899864197},{"id":"https://openalex.org/keywords/anderson-localization","display_name":"Anderson localization","score":0.7699999809265137},{"id":"https://openalex.org/keywords/localization-length","display_name":"localization length","score":0.8489999771118164},{"id":"https://openalex.org/keywords/crossover-scaling","display_name":"crossover scaling","score":0.675000011920929},{"id":"https://openalex.org/keywords/long-range-correlations","display_name":"long-range correlations","score":0.7179999947547913},{"id":"https://openalex.org/keywords/thermalization","display_name":"thermalization","score":0.5490000247955322},{"id":"https://openalex.org/keywords/integrability-breaking","display_name":"integrability breaking","score":0.9350000023841858}],"concepts":[{"id":"https://openalex.org/C2780843604","wikidata":"https://www.wikidata.org/wiki/Q7269515","display_name":"Quasiperiodicity","level":3,"score":0.9746000170707703},{"id":"https://openalex.org/C55637507","wikidata":"https://www.wikidata.org/wiki/Q5870963","display_name":"Quasiperiodic function","level":2,"score":0.9641000032424927},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.8148000240325928},{"id":"https://openalex.org/C122507166","wikidata":"https://www.wikidata.org/wiki/Q628906","display_name":"Crossover","level":2,"score":0.6664999723434448},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5774000287055969},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5514000058174133},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4968000054359436},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4959999918937683},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.47760000824928284},{"id":"https://openalex.org/C2988430800","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Scaling law","level":3,"score":0.47099998593330383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44339999556541443},{"id":"https://openalex.org/C133654230","wikidata":"https://www.wikidata.org/wiki/Q491409","display_name":"Anderson localization","level":2,"score":0.42800000309944153},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.41909998655319214},{"id":"https://openalex.org/C169345407","wikidata":"https://www.wikidata.org/wiki/Q8216221","display_name":"Uncorrelated","level":2,"score":0.4049000144004822},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.3986000120639801},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.3644999861717224},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3310000002384186},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3248000144958496},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C203101518","wikidata":"https://www.wikidata.org/wiki/Q263214","display_name":"Quasicrystal","level":2,"score":0.27559998631477356}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1103/yf98-5fv6","doi":"https://doi.org/10.1103/yf98-5fv6","is_oa":false,"landing_page_url":"https://doi.org/10.1103/yf98-5fv6","pdf_url":null,"source":{"id":"https://openalex.org/S4210235286","display_name":"Physical review. E","issn_l":"2470-0045","issn":["2470-0045","2470-0053","2470-0061"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2607.14549","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.14549","pdf_url":"https://arxiv.org/pdf/2607.14549","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.2607.14549","doi":"https://doi.org/10.48550/arxiv.2607.14549","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.14549","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:2607.14549","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.14549","pdf_url":"https://arxiv.org/pdf/2607.14549","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":[{"id":"https://openalex.org/G1369937091","display_name":null,"funder_award_id":"IBS- R024-D1","funder_id":"https://openalex.org/F4320326441","funder_display_name":"Institute for Basic Science"},{"id":"https://openalex.org/G239391342","display_name":null,"funder_award_id":"IBS-R041-D1-2026-a00","funder_id":"https://openalex.org/F4320326441","funder_display_name":"Institute for Basic Science"},{"id":"https://openalex.org/G4362375936","display_name":null,"funder_award_id":"IBS-R041-D1","funder_id":"https://openalex.org/F4320326441","funder_display_name":"Institute for Basic Science"},{"id":"https://openalex.org/G8805052026","display_name":null,"funder_award_id":"12247101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320326441","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7169558227.pdf","grobid_xml":"https://content.openalex.org/works/W7169558227.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7140329834"],"related_works":["https://openalex.org/W4393151464","https://openalex.org/W4220804300","https://openalex.org/W3197511720","https://openalex.org/W1981673189","https://openalex.org/W4385803815","https://openalex.org/W4308244817","https://openalex.org/W2080797393","https://openalex.org/W4406449527","https://openalex.org/W4409362149","https://openalex.org/W4221165253"],"abstract_inverted_index":{"We":[0,17],"study":[1],"the":[2,12,20,28,35,38,55,58,70,79,88,115,129,135],"Lyapunov":[3],"spectrum":[4],"scaling":[5,26,80],"of":[6,14,40,54,73,109,118,122,131,137],"thermal":[7],"weakly-nonlinear":[8],"unitary":[9],"maps":[10],"in":[11,128,134],"presence":[13,130],"quasiperiodic":[15,123],"potentials.":[16],"search":[18],"for":[19,57],"crossover":[21,81],"from":[22],"long-range":[23],"to":[24,37,99],"short-range":[25],"as":[27,85,97],"localization":[29,67],"length":[30],"\u03be":[31],"decreases":[32],"and":[33,102,140],"compare":[34],"details":[36],"case":[39,60,136],"uncorrelated":[41],"Anderson":[42,100],"disorder":[43],"[Phys.":[44],"Rev.":[45],"Res.":[46],"6":[47],"L012064":[48],"(2024)].":[49],"A":[50],"comparative":[51],"statistical":[52],"analysis":[53,90],"eigenstates":[56],"linear":[59],"shows":[61,91],"that":[62,78,92],"quasiperiodicity":[63],"has":[64],"a":[65],"stronger":[66],"impact":[68,117],"at":[69,105,114],"same":[71],"value":[72],"\u03be.":[74,110],"Therefore":[75],"we":[76],"expect":[77],"should":[82],"be":[83],"enhanced":[84],"well.":[86],"However,":[87],"numerical":[89],"it":[93],"is":[94,103],"strongly":[95],"delayed":[96],"compared":[98],"disorder,":[101],"observed":[104],"anomalously":[106],"small":[107],"values":[108],"These":[111],"findings":[112],"hint":[113],"potential":[116],"long":[119],"range":[120],"correlations":[121],"localized":[124],"eigenstates,":[125],"which":[126],"persist":[127],"interactions":[132],"even":[133],"integrability":[138],"breaking":[139],"thermalization.":[141]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-07-18T00:00:00"}