{"id":"https://openalex.org/W4226265362","doi":"https://doi.org/10.3390/sym14020183","title":"Rearrangement of Energy Levels between Energy Super-Bands Characterized by Second Chern Class","display_name":"Rearrangement of Energy Levels between Energy Super-Bands Characterized by Second Chern Class","publication_year":2022,"publication_date":"2022-01-18","ids":{"openalex":"https://openalex.org/W4226265362","doi":"https://doi.org/10.3390/sym14020183"},"language":"en","primary_location":{"id":"doi:10.3390/sym14020183","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020183","pdf_url":"https://www.mdpi.com/2073-8994/14/2/183/pdf?version=1642475611","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/2/183/pdf?version=1642475611","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051795491","display_name":"D. A. Sadovski\u0131\u0301","orcid":"https://orcid.org/0000-0002-4611-6469"},"institutions":[{"id":"https://openalex.org/I4210101037","display_name":"Laboratoire de Physico-Chimie de l'Atmosph\u00e8re","ror":"https://ror.org/014net767","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2802487185","https://openalex.org/I4210101037","https://openalex.org/I4210137101","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dmitrii Sadovskii","raw_affiliation_strings":["Laboratoire de Physico-Chimie de l\u2019Atmosph\u00e8re, UR4493, LPCA, Universit\u00e9 du Littoral C\u00f4te d\u2019Opale, F-59140 Dunkerque, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Physico-Chimie de l\u2019Atmosph\u00e8re, UR4493, LPCA, Universit\u00e9 du Littoral C\u00f4te d\u2019Opale, F-59140 Dunkerque, France","institution_ids":["https://openalex.org/I4210101037"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090681857","display_name":"B.I. Z\u0125ilinski\u0131\u0301","orcid":null},"institutions":[{"id":"https://openalex.org/I4210101037","display_name":"Laboratoire de Physico-Chimie de l'Atmosph\u00e8re","ror":"https://ror.org/014net767","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2802487185","https://openalex.org/I4210101037","https://openalex.org/I4210137101","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Boris Zhilinskii","raw_affiliation_strings":["Laboratoire de Physico-Chimie de l\u2019Atmosph\u00e8re, UR4493, LPCA, Universit\u00e9 du Littoral C\u00f4te d\u2019Opale, F-59140 Dunkerque, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Physico-Chimie de l\u2019Atmosph\u00e8re, UR4493, LPCA, Universit\u00e9 du Littoral C\u00f4te d\u2019Opale, F-59140 Dunkerque, France","institution_ids":["https://openalex.org/I4210101037"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090681857"],"corresponding_institution_ids":["https://openalex.org/I4210101037"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2499,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.48975261,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"14","issue":"2","first_page":"183","last_page":"183"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.9994999766349792,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9991000294685364,"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/T10657","display_name":"Topological Materials and Phenomena","score":0.9983000159263611,"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/chern-class","display_name":"Chern class","score":0.6988003253936768},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5736522674560547},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5594954490661621},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5481671094894409},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.5385653972625732},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5171236991882324},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5111282467842102},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.44414186477661133},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.4392394423484802},{"id":"https://openalex.org/keywords/quantum-number","display_name":"Quantum number","score":0.4253648817539215},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3842029869556427},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.33952024579048157},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.33342987298965454}],"concepts":[{"id":"https://openalex.org/C151527765","wikidata":"https://www.wikidata.org/wiki/Q1069818","display_name":"Chern class","level":2,"score":0.6988003253936768},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5736522674560547},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5594954490661621},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5481671094894409},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.5385653972625732},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5171236991882324},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5111282467842102},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.44414186477661133},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4392394423484802},{"id":"https://openalex.org/C174038435","wikidata":"https://www.wikidata.org/wiki/Q232431","display_name":"Quantum number","level":2,"score":0.4253648817539215},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3842029869556427},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.33952024579048157},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.33342987298965454},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym14020183","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020183","pdf_url":"https://www.mdpi.com/2073-8994/14/2/183/pdf?version=1642475611","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04290974v1","is_oa":true,"landing_page_url":"https://ulco.hal.science/hal-04290974","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, 2022, 14 (2), pp.183. ⟨10.3390/sym14020183⟩","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:9e43f4d0948e4cfab70d39d2a76c5149","is_oa":true,"landing_page_url":"https://doaj.org/article/9e43f4d0948e4cfab70d39d2a76c5149","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":"Symmetry, Vol 14, Iss 2, p 183 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/2/183/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14020183","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14020183","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020183","pdf_url":"https://www.mdpi.com/2073-8994/14/2/183/pdf?version=1642475611","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.699999988079071,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4226265362.pdf","grobid_xml":"https://content.openalex.org/works/W4226265362.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1543478369","https://openalex.org/W1571300791","https://openalex.org/W1963577893","https://openalex.org/W1965292581","https://openalex.org/W1972043045","https://openalex.org/W1981440158","https://openalex.org/W1986481838","https://openalex.org/W2001661873","https://openalex.org/W2002804025","https://openalex.org/W2007242923","https://openalex.org/W2011986905","https://openalex.org/W2012486161","https://openalex.org/W2028785431","https://openalex.org/W2031119305","https://openalex.org/W2047034598","https://openalex.org/W2060568148","https://openalex.org/W2081112065","https://openalex.org/W2088163399","https://openalex.org/W2097780038","https://openalex.org/W2110476892","https://openalex.org/W2127494126","https://openalex.org/W2159843440","https://openalex.org/W2160473004","https://openalex.org/W2184903846","https://openalex.org/W2502880094","https://openalex.org/W2569113128","https://openalex.org/W2885571923","https://openalex.org/W2963167987","https://openalex.org/W2984876276","https://openalex.org/W3035155392","https://openalex.org/W3046046606","https://openalex.org/W3100575977","https://openalex.org/W3101432261","https://openalex.org/W4248945936","https://openalex.org/W4250056050","https://openalex.org/W6600539481","https://openalex.org/W6781855423"],"related_works":["https://openalex.org/W2372940580","https://openalex.org/W2101113459","https://openalex.org/W2187706389","https://openalex.org/W2160348827","https://openalex.org/W1970824047","https://openalex.org/W1941883603","https://openalex.org/W1842556415","https://openalex.org/W4252688432","https://openalex.org/W2895423135","https://openalex.org/W2021019993"],"abstract_inverted_index":{"We":[0,64],"generalize":[1],"the":[2,6,12,24,40,61,67,74,77,85,99,104,110,114,128,133,140,147],"dynamical":[3,21,58],"analog":[4],"of":[5,15,60,76,80,84,87,113,121,132,142,156],"Berry":[7],"geometric":[8],"phase":[9],"setup":[10],"to":[11,56],"quaternionic":[13,22],"model":[14,36,82],"Avron":[16],"et":[17],"al.":[18],"In":[19],"our":[20,81],"system,":[23],"fast":[25],"half-integer":[26],"spin":[27,46],"subsystem":[28],"interacts":[29],"with":[30,73,109],"a":[31,154],"slow":[32,62],"two-degrees-of-freedom":[33],"subsystem.":[34,63],"The":[35,137],"is":[37,49,120,125,151],"invariant":[38],"under":[39],"1:1:2":[41],"weighted":[42],"SO(2)":[43],"symmetry":[44],"and":[45,124,146],"inversion.":[47],"There":[48],"one":[50,88],"formal":[51,100],"control":[52,101],"parameter":[53,102],"in":[54],"addition":[55],"four":[57],"variables":[59],"demonstrate":[65],"that":[66],"most":[68],"elementary":[69],"qualitative":[70,118],"phenomenon":[71,119],"associated":[72,108,134],"rearrangement":[75,86],"energy":[78,89,93,144],"super-bands":[79],"consists":[83],"level":[90],"between":[91,139],"two":[92],"superbands":[94],"which":[95],"takes":[96,103],"place":[97],"when":[98],"special":[105],"isolated":[106],"value":[107],"conical":[111],"degeneracy":[112],"semi-quantum":[115,135],"eigenvalues.":[116],"This":[117],"topological":[122],"origin,":[123],"characterized":[126],"by":[127],"second":[129,148],"Chern":[130,149],"class":[131],"system.":[136],"correspondence":[138],"number":[141,150],"redistributed":[143],"levels":[145],"confirmed":[152],"through":[153],"series":[155],"examples.":[157]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}