{"id":"https://openalex.org/W7221785239","doi":"https://doi.org/10.48550/arxiv.2610.15753","title":"Approaching Irrational Quantization","display_name":"Approaching Irrational Quantization","publication_year":2026,"publication_date":"2026-10-11","ids":{"openalex":"https://openalex.org/W7221785239","doi":"https://doi.org/10.48550/arxiv.2610.15753"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.15753","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.15753","pdf_url":"https://arxiv.org/pdf/2610.15753","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.15753","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064009579","display_name":"Zhihong Wu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wu, Zhihong","raw_affiliation_strings":["International Center for Quantum Materials , School of Physics , Peking University , Beijing , 100871 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"International Center for Quantum Materials , School of Physics , Peking University , Beijing , 100871 , China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5158759213","display_name":"Zhimou Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Zhimou","raw_affiliation_strings":["International Center for Quantum Materials , School of Physics , Peking University , Beijing , 100871 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"International Center for Quantum Materials , School of Physics , Peking University , Beijing , 100871 , China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124015765","display_name":"Siyuan Zhang","orcid":"https://orcid.org/0000-0001-7045-0865","observed_orcids":["https://orcid.org/0000-0001-7045-0865"]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Siyuan","raw_affiliation_strings":["International Center for Quantum Materials , School of Physics , Peking University , Beijing , 100871 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"International Center for Quantum Materials , School of Physics , Peking University , Beijing , 100871 , China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101663525","display_name":"Jinyang Chen","orcid":"https://orcid.org/0000-0001-6330-371X","observed_orcids":["https://orcid.org/0000-0001-6330-371X"]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Jinyang","raw_affiliation_strings":["International Center for Quantum Materials , School of Physics , Peking University , Beijing , 100871 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"International Center for Quantum Materials , School of Physics , Peking University , Beijing , 100871 , China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137423080","display_name":"L. N. Pfeiffer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pfeiffer, L. N.","raw_affiliation_strings":["Department of Electrical Engineering , Princeton University , Princeton , New Jersey , 08544 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering , Princeton University , Princeton , New Jersey , 08544 , USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5158716761","display_name":"K. W. West","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"West, K. W.","raw_affiliation_strings":["Department of Electrical Engineering , Princeton University , Princeton , New Jersey , 08544 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering , Princeton University , Princeton , New Jersey , 08544 , USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5158770188","display_name":"Yang Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Yang","raw_affiliation_strings":["Hefei National Laboratory , Hefei , 230088 , China","International Center for Quantum Materials , School of Physics , Peking University , Beijing , 100871 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hefei National Laboratory , Hefei , 230088 , China","institution_ids":[]},{"raw_affiliation_string":"International Center for Quantum Materials , School of Physics , Peking University , Beijing , 100871 , China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5158742189","display_name":"Xi Lin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Xi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"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/T10382","display_name":"Quantum and electron transport phenomena","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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/T10382","display_name":"Quantum and electron transport phenomena","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T13531","display_name":"Surface and Thin Film Phenomena","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T10657","display_name":"Topological Materials and Phenomena","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/quantum-hall-effect","display_name":"quantum Hall effect","score":0.8320000171661377},{"id":"https://openalex.org/keywords/fractional-quantum-hall-effect","display_name":"fractional quantum Hall effect","score":0.875},{"id":"https://openalex.org/keywords/geometric-networks","display_name":"geometric networks","score":0.6259999871253967},{"id":"https://openalex.org/keywords/landau-levels","display_name":"Landau levels","score":0.6930000185966492},{"id":"https://openalex.org/keywords/geometric-control-theory","display_name":"geometric control","score":0.3319999873638153}],"concepts":[{"id":"https://openalex.org/C94931360","wikidata":"https://www.wikidata.org/wiki/Q607728","display_name":"Irrational number","level":2,"score":0.86080002784729},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.7648000121116638},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.71670001745224},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5008000135421753},{"id":"https://openalex.org/C143397304","wikidata":"https://www.wikidata.org/wiki/Q630426","display_name":"Geometric quantization","level":5,"score":0.4514999985694885},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.43369999527931213},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.42320001125335693},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4034999907016754},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3822000026702881},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.3560999929904938},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34929999709129333},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.33379998803138733},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2551000118255615},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.2549999952316284}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.15753","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.15753","pdf_url":"https://arxiv.org/pdf/2610.15753","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.2610.15753","doi":"https://doi.org/10.48550/arxiv.2610.15753","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.15753","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:2610.15753","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.15753","pdf_url":"https://arxiv.org/pdf/2610.15753","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/G1101424248","display_name":null,"funder_award_id":"2021YFA1401900","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G1776380517","display_name":null,"funder_award_id":"2021ZD0302600","funder_id":"https://openalex.org/F4320329860","funder_display_name":"National Science and Technology Major Project"},{"id":"https://openalex.org/G2590390272","display_name":null,"funder_award_id":"2021YFA1401900","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2879615561","display_name":"Supplying the community with high-mobility quantum wells and polaritonic devices","funder_award_id":"GBMF14260","funder_id":"https://openalex.org/F4320306202","funder_display_name":"Gordon and Betty Moore Foundation"},{"id":"https://openalex.org/G3014714261","display_name":null,"funder_award_id":"12141001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306202","display_name":"Gordon and Betty Moore Foundation","ror":"https://ror.org/006wxqw41"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324787","display_name":"Peking University","ror":"https://ror.org/02v51f717"},{"id":"https://openalex.org/F4320329860","display_name":"National Science and Technology Major Project","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221785239.pdf","grobid_xml":"https://content.openalex.org/works/W7221785239.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2032958914","https://openalex.org/W4256159658","https://openalex.org/W1619577885","https://openalex.org/W2991156502","https://openalex.org/W7128544528","https://openalex.org/W2949700953","https://openalex.org/W7100163987","https://openalex.org/W7100019336","https://openalex.org/W4298706910","https://openalex.org/W789446702"],"abstract_inverted_index":{"The":[0,105],"integer":[1,14],"and":[2,15,96,135],"fractional":[3,16],"quantum":[4],"Hall":[5],"effects":[6],"reveal":[7],"that":[8,39,137],"quantized":[9,42,140],"physical":[10,148],"responses":[11],"can":[12,27,44,142],"take":[13],"values,":[17],"respectively.":[18],"This":[19],"naturally":[20],"raises":[21],"the":[22,47,92,121,128],"question":[23],"of":[24,50,70,130],"whether":[25],"quantization":[26,131],"extend":[28,127],"beyond":[29,132],"rational":[30,133],"numbers":[31],"to":[32,91],"an":[33,76,138],"irrational":[34,93,139],"value.":[35],"Here":[36],"we":[37,82],"show":[38],"such":[40],"a":[41,51,59,68,84,98,115,146],"response":[43,141],"emerge":[45],"from":[46],"limiting":[48],"behavior":[49],"finite,":[52],"experimentally":[53],"realizable":[54],"geometric":[55,64,103],"network.":[56],"We":[57],"develop":[58],"method":[60],"based":[61],"on":[62],"infinite":[63,77],"structures,":[65],"in":[66,120],"which":[67],"sequence":[69],"finite":[71,99,147],"networks":[72],"rapidly":[73],"converges":[74,90],"toward":[75],"limit.":[78],"Following":[79],"this":[80],"approach,":[81],"identify":[83],"planar":[85],"network":[86],"whose":[87],"normalized":[88,107],"resistance":[89,108],"value":[94],"$\\sqrt{3}$,":[95],"realize":[97],"approximation":[100],"with":[101],"high-precision":[102],"control.":[104],"measured":[106],"is":[109],"$1.735":[110],"\\pm":[111],"0.001\\,":[112],"h/e^2$":[113],"for":[114],"fully":[116],"occupied":[117],"Landau":[118],"level":[119],"designed":[122],"pattern.":[123],"Our":[124],"experimental":[125],"results":[126],"concept":[129],"values":[134],"demonstrate":[136],"be":[143],"approached":[144],"through":[145],"system.":[149]},"counts_by_year":[],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2026-10-15T00:00:00"}