{"id":"https://openalex.org/W2947637745","doi":"https://doi.org/10.1103/physreva.99.062112","title":"Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling","display_name":"Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling","publication_year":2019,"publication_date":"2019-06-19","ids":{"openalex":"https://openalex.org/W2947637745","doi":"https://doi.org/10.1103/physreva.99.062112","mag":"2947637745"},"language":"en","primary_location":{"id":"doi:10.1103/physreva.99.062112","doi":"https://doi.org/10.1103/physreva.99.062112","is_oa":true,"landing_page_url":"https://doi.org/10.1103/physreva.99.062112","pdf_url":null,"source":{"id":"https://openalex.org/S164566984","display_name":"Physical Review A","issn_l":"0556-2791","issn":["0556-2791","1050-2947","1094-1622","1538-4446","2469-9926","2469-9934","2469-9942"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","norway-2","poland-100","poland-70","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review A","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1103/physreva.99.062112","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023582561","display_name":"P. Wang","orcid":"https://orcid.org/0000-0001-5315-9996","observed_orcids":["https://orcid.org/0000-0001-5315-9996"]},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"P. Wang","raw_affiliation_strings":["School of Physics, Nankai University, Tianjin 300071, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics, Nankai University, Tianjin 300071, China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021454328","display_name":"L. Jin","orcid":"https://orcid.org/0000-0003-1898-6317","observed_orcids":["https://orcid.org/0000-0003-1898-6317"]},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"L. Jin","raw_affiliation_strings":["School of Physics, Nankai University, Tianjin 300071, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics, Nankai University, Tianjin 300071, China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013254314","display_name":"Z. Song","orcid":"https://orcid.org/0000-0002-3315-4589","observed_orcids":["https://orcid.org/0000-0002-3315-4589"]},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Z. Song","raw_affiliation_strings":["School of Physics, Nankai University, Tianjin 300071, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics, Nankai University, Tianjin 300071, China","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I205237279"],"apc_list":{"value":2675,"currency":"USD","value_usd":2675},"apc_paid":{"value":2675,"currency":"USD","value_usd":2675},"fwci":2.7421,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.91830028,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"99","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9994999766349792,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9994999766349792,"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":9.999999747378752e-05,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/non-hermitian-phase-transition","display_name":"non-Hermitian phase transition","score":0.9940000176429749},{"id":"https://openalex.org/keywords/asymmetric-coupling","display_name":"asymmetric coupling","score":0.9269999861717224},{"id":"https://openalex.org/keywords/eigenstate-localization","display_name":"eigenstate localization","score":0.8809999823570251},{"id":"https://openalex.org/keywords/open-boundaries","display_name":"open boundaries","score":0.5230000019073486},{"id":"https://openalex.org/keywords/translation-invariance","display_name":"translation invariance","score":0.7239999771118164},{"id":"https://openalex.org/keywords/scaling-laws","display_name":"scaling laws","score":0.6069999933242798}],"concepts":[{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7175833582878113},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.695689857006073},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5373965501785278},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.5179926156997681},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.46274876594543457},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4440914988517761},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4384540915489197},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.42383551597595215},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.4218539595603943},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.37383297085762024},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.06519362330436707},{"id":"https://openalex.org/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1103/physreva.99.062112","doi":"https://doi.org/10.1103/physreva.99.062112","is_oa":true,"landing_page_url":"https://doi.org/10.1103/physreva.99.062112","pdf_url":null,"source":{"id":"https://openalex.org/S164566984","display_name":"Physical Review A","issn_l":"0556-2791","issn":["0556-2791","1050-2947","1094-1622","1538-4446","2469-9926","2469-9934","2469-9942"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","norway-2","poland-100","poland-70","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review A","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1906.00610","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1906.00610","pdf_url":"https://arxiv.org/pdf/1906.00610","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:figshare.com:article/24689436","doi":null,"is_oa":true,"landing_page_url":"https://figshare.com/articles/preprint/Non-Hermitian_phase_transition_and_eigenstate_localization_induced_by_asymmetric_coupling/24689436","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":null,"raw_type":"Text"},{"id":"doi:10.48550/arxiv.1906.00610","doi":"https://doi.org/10.48550/arxiv.1906.00610","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1906.00610","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":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1103/physreva.99.062112","doi":"https://doi.org/10.1103/physreva.99.062112","is_oa":true,"landing_page_url":"https://doi.org/10.1103/physreva.99.062112","pdf_url":null,"source":{"id":"https://openalex.org/S164566984","display_name":"Physical Review A","issn_l":"0556-2791","issn":["0556-2791","1050-2947","1094-1622","1538-4446","2469-9926","2469-9934","2469-9942"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","norway-2","poland-100","poland-70","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review A","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4099999964237213}],"study_designs":[],"awards":[{"id":"https://openalex.org/G1281191304","display_name":null,"funder_award_id":"63191522","funder_id":"https://openalex.org/F4320323021","funder_display_name":"Nankai University"},{"id":"https://openalex.org/G7656028237","display_name":"\u591a\u4f53\u7cfb\u7edf\u91cf\u5b50\u6001\u7684\u52a8\u529b\u5b66\u63a2\u6d4b\u5236\u5907\u7814\u7a76","funder_award_id":"11874225","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G9000110663","display_name":null,"funder_award_id":"11605094","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G927696288","display_name":null,"funder_award_id":"63191738","funder_id":"https://openalex.org/F4320323021","funder_display_name":"Nankai University"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323021","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":141,"referenced_works":["https://openalex.org/W1531935167","https://openalex.org/W1584140214","https://openalex.org/W1625951388","https://openalex.org/W1649271673","https://openalex.org/W1665371518","https://openalex.org/W1679473116","https://openalex.org/W1870420882","https://openalex.org/W1911454827","https://openalex.org/W1911969426","https://openalex.org/W1978986114","https://openalex.org/W1979129168","https://openalex.org/W1986716158","https://openalex.org/W1995387414","https://openalex.org/W1997323544","https://openalex.org/W1999786383","https://openalex.org/W2000359448","https://openalex.org/W2005869052","https://openalex.org/W2006869939","https://openalex.org/W2015027166","https://openalex.org/W2022671832","https://openalex.org/W2024786641","https://openalex.org/W2027718107","https://openalex.org/W2047699813","https://openalex.org/W2048581228","https://openalex.org/W2050538992","https://openalex.org/W2054153719","https://openalex.org/W2062265521","https://openalex.org/W2065499715","https://openalex.org/W2066202639","https://openalex.org/W2073111078","https://openalex.org/W2075542354","https://openalex.org/W2085072709","https://openalex.org/W2117062221","https://openalex.org/W2121853028","https://openalex.org/W2126665790","https://openalex.org/W2139191007","https://openalex.org/W2142869914","https://openalex.org/W2150440056","https://openalex.org/W2151014458","https://openalex.org/W2152074534","https://openalex.org/W2159798643","https://openalex.org/W2160223254","https://openalex.org/W2166080990","https://openalex.org/W2240187636","https://openalex.org/W2260384802","https://openalex.org/W2273068609","https://openalex.org/W2286173540","https://openalex.org/W2291084434","https://openalex.org/W2301906456","https://openalex.org/W2322396586","https://openalex.org/W2336564914","https://openalex.org/W2338277331","https://openalex.org/W2341719212","https://openalex.org/W2343724168","https://openalex.org/W2411321572","https://openalex.org/W2411481865","https://openalex.org/W2412395139","https://openalex.org/W2413829636","https://openalex.org/W2514420608","https://openalex.org/W2538420542","https://openalex.org/W2548501878","https://openalex.org/W2560262202","https://openalex.org/W2560562419","https://openalex.org/W2599769001","https://openalex.org/W2620778762","https://openalex.org/W2621465889","https://openalex.org/W2626594927","https://openalex.org/W2656144764","https://openalex.org/W2733896976","https://openalex.org/W2734969118","https://openalex.org/W2744045251","https://openalex.org/W2744151324","https://openalex.org/W2750609812","https://openalex.org/W2751538914","https://openalex.org/W2752472685","https://openalex.org/W2752539361","https://openalex.org/W2754319903","https://openalex.org/W2765531843","https://openalex.org/W2768107904","https://openalex.org/W2769934158","https://openalex.org/W2775352217","https://openalex.org/W2781491230","https://openalex.org/W2782079035","https://openalex.org/W2784208533","https://openalex.org/W2785864340","https://openalex.org/W2785994263","https://openalex.org/W2786312866","https://openalex.org/W2787166448","https://openalex.org/W2787371208","https://openalex.org/W2787598276","https://openalex.org/W2788022603","https://openalex.org/W2790056669","https://openalex.org/W2791270389","https://openalex.org/W2793448389","https://openalex.org/W2795025044","https://openalex.org/W2795729525","https://openalex.org/W2796030277","https://openalex.org/W2796102228","https://openalex.org/W2798243928","https://openalex.org/W2799267003","https://openalex.org/W2800561807","https://openalex.org/W2803613909","https://openalex.org/W2804626498","https://openalex.org/W2804805963","https://openalex.org/W2807043350","https://openalex.org/W2807779697","https://openalex.org/W2809792529","https://openalex.org/W2810753830","https://openalex.org/W2817128990","https://openalex.org/W2838327813","https://openalex.org/W2883436585","https://openalex.org/W2884406639","https://openalex.org/W2888032628","https://openalex.org/W2890702314","https://openalex.org/W2891240270","https://openalex.org/W2894888707","https://openalex.org/W2894914636","https://openalex.org/W2895070529","https://openalex.org/W2895382711","https://openalex.org/W2895789785","https://openalex.org/W2897123535","https://openalex.org/W2898648835","https://openalex.org/W2899338428","https://openalex.org/W2900507081","https://openalex.org/W2900740345","https://openalex.org/W2901297113","https://openalex.org/W2902536335","https://openalex.org/W2903354357","https://openalex.org/W2905588081","https://openalex.org/W2906569305","https://openalex.org/W2908224353","https://openalex.org/W2908266731","https://openalex.org/W2909400771","https://openalex.org/W2916412555","https://openalex.org/W2945061864","https://openalex.org/W2949964692","https://openalex.org/W2950613702","https://openalex.org/W2951258766","https://openalex.org/W3104668646","https://openalex.org/W3105326770","https://openalex.org/W3147245560"],"related_works":["https://openalex.org/W3196977684","https://openalex.org/W3104367283","https://openalex.org/W4317464059","https://openalex.org/W4378757502","https://openalex.org/W4385248177","https://openalex.org/W4244117186","https://openalex.org/W2994793674","https://openalex.org/W2950761947","https://openalex.org/W1635499494","https://openalex.org/W2011113005"],"abstract_inverted_index":{"We":[0],"investigate":[1],"a":[2,16,26,41,113],"uniformly":[3],"coupled":[4],"non-Hermitian":[5,42,92,105,110,123],"system":[6],"with":[7,112],"asymmetric":[8,12,77],"coupling":[9,13,18,78,115],"amplitude.":[10],"The":[11,58],"equals":[14],"to":[15,34,72],"symmetric":[17],"threaded":[19],"by":[20],"an":[21,35,46,55],"imaginary":[22,30,36,50,84],"gauge":[23,31,51],"field.":[24],"In":[25],"closed":[27],"configuration,":[28],"the":[29,49,66,74,83,91,104,109,122],"field":[32,52],"leads":[33],"magnetic":[37,85],"flux,":[38],"which":[39,100],"induces":[40],"phase":[43,93,106,124],"transition.":[44],"For":[45],"open":[47],"boundary,":[48],"results":[53],"in":[54,108],"eigenstate":[56],"localization.":[57,128],"eigenstates":[59],"under":[60],"Dirac":[61],"and":[62,65,126],"biorthogonal":[63],"norms":[64],"scaling":[67],"laws":[68],"are":[69],"quantitatively":[70],"investigated":[71],"show":[73],"affect":[75],"of":[76],"induced":[79],"one-way":[80,127],"amplification.":[81],"However,":[82],"flux":[86],"does":[87],"not":[88],"inevitably":[89],"induce":[90],"transition":[94,107,125],"for":[95],"systems":[96],"without":[97],"translation":[98],"invariance,":[99],"is":[101],"elucidated":[102],"from":[103],"ring":[111],"single":[114],"defect.":[116],"Our":[117],"findings":[118],"provide":[119],"insights":[120],"into":[121]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2019-06-07T00:00:00"}
