{"id":"https://openalex.org/W2425951871","doi":null,"title":"Bloch theorem for the evolution of states in a cyclic quantum system and a new type of quantum phases","display_name":"Bloch theorem for the evolution of states in a cyclic quantum system and a new type of quantum phases","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2425951871","mag":"2425951871"},"language":"en","primary_location":{"id":"mag:2425951871","doi":null,"is_oa":false,"landing_page_url":"http://www.irgrid.ac.cn/handle/1471x/786654","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027169296","display_name":"BZ Li","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"BZ Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076716558","display_name":"Yan Fl","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yan Fl","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102128859","display_name":"JH Wu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"JH Wu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5026717183","display_name":"J.-Q. Liang","orcid":"https://orcid.org/0000-0003-2985-6040","observed_orcids":["https://orcid.org/0000-0003-2985-6040"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J.-Q. Liang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2985-6040","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":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.26762359,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"39","issue":"9","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9282000064849854,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9282000064849854,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.028999999165534973,"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/T11804","display_name":"Quantum many-body systems","score":0.006899999920278788,"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/bloch-s-theorem","display_name":"Bloch theorem","score":0.9700000286102295},{"id":"https://openalex.org/keywords/time-dependent-schrodinger-equation","display_name":"time-dependent Schr\u00f6dinger equation","score":0.9380000233650208},{"id":"https://openalex.org/keywords/bloch-functions","display_name":"Bloch functions","score":0.75},{"id":"https://openalex.org/keywords/aharonov-anandan-phase","display_name":"Aharonov-Anandan phase","score":0.8840000033378601},{"id":"https://openalex.org/keywords/berry-phase","display_name":"Berry phase","score":0.996999979019165},{"id":"https://openalex.org/keywords/adiabatic-approximation","display_name":"adiabatic approximation","score":0.9589999914169312},{"id":"https://openalex.org/keywords/spin-precession","display_name":"spin precession","score":0.7049999833106995}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.5238311886787415},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.5161774754524231},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5107872486114502},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.5004346370697021},{"id":"https://openalex.org/C109663097","wikidata":"https://www.wikidata.org/wiki/Q182453","display_name":"Adiabatic process","level":2,"score":0.4740355312824249},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4700832664966583},{"id":"https://openalex.org/C136277988","wikidata":"https://www.wikidata.org/wiki/Q884593","display_name":"Bloch sphere","level":4,"score":0.469268262386322},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4171420931816101},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.41239264607429504},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36677247285842896},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.07730376720428467},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"mag:2425951871","doi":null,"is_oa":false,"landing_page_url":"http://www.irgrid.ac.cn/handle/1471x/786654","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"mag:3152045722","doi":null,"is_oa":false,"landing_page_url":"http://en.cnki.com.cn/Article_en/CJFDTOTAL-JAXG199609007.htm","pdf_url":null,"source":{"id":"https://openalex.org/S18344391","display_name":"Science China Mathematics","issn_l":"1869-1862","issn":["1869-1862","1674-7283"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"\u4e2d\u56fd\u79d1\u5b66A\u8f91(\u82f1\u6587\u7248)","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2595601678","https://openalex.org/W2033647518","https://openalex.org/W1990631010","https://openalex.org/W1967092709","https://openalex.org/W4246014226","https://openalex.org/W2135602248","https://openalex.org/W2044154336","https://openalex.org/W2180253007","https://openalex.org/W2095568539","https://openalex.org/W2043649022"],"abstract_inverted_index":{"It":[0],"is":[1,81,106],"found":[2],"that":[3],"in":[4,97],"a":[5,45,98],"quantum":[6,49],"system":[7],"with":[8,27,102],"cyclic":[9],"Hamiltonian":[10],"the":[11,16,22,30,39,58,61,68,72,76,91],"time-dependent":[12],"Schrodinger":[13],"equation":[14],"admits":[15],"Bloch":[17,25,55],"type":[18,47],"solutions":[19,33],"which":[20],"have":[21],"form":[23],"of":[24,38,48,78,93],"function":[26],"respect":[28],"to":[29,44,67],"time.":[31],"These":[32],"constitute":[34],"an":[35],"orthonormal":[36],"basis":[37],"solution":[40],"space":[41],"and":[42,65,88],"lead":[43],"new":[46,52],"phases.":[50],"The":[51,83],"phases,":[53,64],"called":[54],"phases":[56,70],"by":[57],"authors,":[59],"are":[60,86],"special":[62],"Aharonov-Anandan":[63],"reduce":[66],"Berry":[69],"under":[71],"adiabatic":[73],"approximation":[74],"if":[75],"degeneracy":[77],"instantaneous":[79],"eigenenergy":[80],"time-independent.":[82],"above":[84],"conclusions":[85],"proved":[87],"calculation":[89],"for":[90],"evolution":[92],"spin":[94],"magnetic":[95,99],"moments":[96],"field":[100],"precessing":[101],"constant":[103],"angular":[104],"velocity":[105],"exemplified.":[107]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2016-06-24T00:00:00"}