{"id":"https://openalex.org/W3034616920","doi":"https://doi.org/10.1137/21m1429412","title":"Lower Bound on Quantum Tunneling for Strong Magnetic Fields","display_name":"Lower Bound on Quantum Tunneling for Strong Magnetic Fields","publication_year":2022,"publication_date":"2022-02-01","ids":{"openalex":"https://openalex.org/W3034616920","doi":"https://doi.org/10.1137/21m1429412","mag":"3034616920"},"language":"en","primary_location":{"id":"doi:10.1137/21m1429412","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1429412","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5037466938","display_name":"Charles Fefferman","orcid":"https://orcid.org/0000-0002-9565-6488"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Charles Fefferman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040981258","display_name":"Jacob Shapiro","orcid":"https://orcid.org/0000-0003-0732-393X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jacob Shapiro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5074916646","display_name":"Michael I. Weinstein","orcid":"https://orcid.org/0000-0002-6266-6604"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael I. Weinstein","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-6266-6604","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0035,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.86188784,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"54","issue":"1","first_page":"1105","last_page":"1130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9998000264167786,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9998000264167786,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9997000098228455,"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/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.9994000196456909,"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/quantum-tunnelling","display_name":"Quantum tunnelling","score":0.7460557222366333},{"id":"https://openalex.org/keywords/bound-state","display_name":"Bound state","score":0.7147005796432495},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7146482467651367},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6592680811882019},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6230552792549133},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.5718516111373901},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.5695396065711975},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.42303991317749023},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.40548691153526306},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3762195110321045},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.351759135723114}],"concepts":[{"id":"https://openalex.org/C120398109","wikidata":"https://www.wikidata.org/wiki/Q175751","display_name":"Quantum tunnelling","level":2,"score":0.7460557222366333},{"id":"https://openalex.org/C174084160","wikidata":"https://www.wikidata.org/wiki/Q908049","display_name":"Bound state","level":2,"score":0.7147005796432495},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7146482467651367},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6592680811882019},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6230552792549133},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.5718516111373901},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.5695396065711975},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.42303991317749023},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.40548691153526306},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3762195110321045},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.351759135723114}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1429412","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1429412","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.5400000214576721}],"awards":[{"id":"https://openalex.org/G1011316999","display_name":null,"funder_award_id":"DMS-1620418","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3109860087","display_name":null,"funder_award_id":"P2EZP2_184228","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5510887716","display_name":null,"funder_award_id":"DMS-1908657","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7546795808","display_name":null,"funder_award_id":"376319","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G799854625","display_name":null,"funder_award_id":"DMS-1700180","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G893821387","display_name":null,"funder_award_id":"DMS-1412560","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W590791627","https://openalex.org/W1178443260","https://openalex.org/W1983777807","https://openalex.org/W1998745857","https://openalex.org/W2034459049","https://openalex.org/W2037496189","https://openalex.org/W2038531793","https://openalex.org/W2048472068","https://openalex.org/W2060452329","https://openalex.org/W2062489691","https://openalex.org/W2063221006","https://openalex.org/W2087943808","https://openalex.org/W2090996949","https://openalex.org/W2098661948","https://openalex.org/W2318325762","https://openalex.org/W2469214198","https://openalex.org/W2536474416","https://openalex.org/W2553410669","https://openalex.org/W2565988279","https://openalex.org/W2624886799","https://openalex.org/W2990881817","https://openalex.org/W3094207574","https://openalex.org/W3203337368","https://openalex.org/W4300223101"],"related_works":["https://openalex.org/W2012959172","https://openalex.org/W2064440194","https://openalex.org/W1995707634","https://openalex.org/W2740243652","https://openalex.org/W3182877397","https://openalex.org/W3089234692","https://openalex.org/W1987656551","https://openalex.org/W188510070","https://openalex.org/W3139201437","https://openalex.org/W1633290709"],"abstract_inverted_index":{"We":[0,39],"consider":[1],"a":[2,6,10,15,69,79],"particle":[3],"bound":[4,71],"to":[5,14,31],"two-dimensional":[7],"plane":[8],"and":[9,42,57,101],"double-well":[11],"potential,":[12],"subject":[13],"perpendicular":[16],"uniform":[17],"magnetic":[18,54],"field.":[19],"The":[20,65],"energy":[21],"difference":[22],"between":[23,35,76],"the":[24,32,36,49,53,58,61,73,77],"lowest":[25],"two":[26,37],"eigenvalues---the":[27],"eigenvalue":[28],"splitting---is":[29],"related":[30],"tunneling":[33],"probability":[34],"wells.":[38],"obtain":[40],"upper":[41],"lower":[43,70],"bounds":[44],"on":[45,72],"this":[46],"splitting":[47],"in":[48,82],"regime":[50],"where":[51],"both":[52],"field":[55],"strength":[56],"depth":[59],"of":[60,86],"wells":[62],"are":[63],"large.":[64],"main":[66],"step":[67],"is":[68,103],"hopping":[74],"amplitude":[75],"wells,":[78],"key":[80],"parameter":[81],"tight":[83],"binding":[84],"models":[85],"solid":[87],"state":[88],"physics,":[89],"given":[90],"by":[91],"an":[92],"oscillatory":[93],"integral,":[94],"whose":[95],"phase":[96],"has":[97],"no":[98],"critical":[99],"point":[100],"which":[102],"exponentially":[104],"small.":[105]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
