{"id":"https://openalex.org/W2398955493","doi":"https://doi.org/10.1137/15m1008221","title":"Spectral Asymptotics in One-Dimensional Periodic Lattices with Geometric Interaction","display_name":"Spectral Asymptotics in One-Dimensional Periodic Lattices with Geometric Interaction","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2398955493","doi":"https://doi.org/10.1137/15m1008221","mag":"2398955493"},"language":"en","primary_location":{"id":"doi:10.1137/15m1008221","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1008221","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","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/A5082185891","display_name":"Ioannis Chremmos","orcid":"https://orcid.org/0000-0002-8733-4948"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"funder","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210110240","display_name":"Max Planck Institute for the Science of Light","ror":"https://ror.org/020as7681","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210110240"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Ioannis Chremmos","raw_affiliation_strings":["Sandoghdar Division, Max Planck Institute for the Science of Light, Max Planck Society"],"affiliations":[{"raw_affiliation_string":"Sandoghdar Division, Max Planck Institute for the Science of Light, Max Planck Society","institution_ids":["https://openalex.org/I4210110240","https://openalex.org/I149899117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062242606","display_name":"George Fikioris","orcid":"https://orcid.org/0000-0002-0987-8835"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"George Fikioris","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082185891"],"corresponding_institution_ids":["https://openalex.org/I149899117","https://openalex.org/I4210110240"],"apc_list":null,"apc_paid":null,"fwci":0.4347,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.67590953,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"76","issue":"3","first_page":"950","last_page":"975"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10666","display_name":"Photonic Crystals and Applications","score":0.9995999932289124,"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/T10666","display_name":"Photonic Crystals and Applications","score":0.9995999932289124,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8230374455451965},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.7977895736694336},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.6642374992370605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6613989472389221},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6001993417739868},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5026133060455322},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.460754930973053},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4432843327522278},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.44212600588798523},{"id":"https://openalex.org/keywords/matrix-analysis","display_name":"Matrix analysis","score":0.41993945837020874},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33699896931648254},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21544241905212402},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1941852569580078},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1435454785823822}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8230374455451965},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.7977895736694336},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.6642374992370605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6613989472389221},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6001993417739868},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5026133060455322},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.460754930973053},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4432843327522278},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.44212600588798523},{"id":"https://openalex.org/C149488123","wikidata":"https://www.wikidata.org/wiki/Q17098730","display_name":"Matrix analysis","level":3,"score":0.41993945837020874},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33699896931648254},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21544241905212402},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1941852569580078},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1435454785823822},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/15m1008221","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1008221","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:pure.mpg.de:item_2446031","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-002D-6E19-0","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON APPLIED MATHEMATICS","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.6100000143051147,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W149522324","https://openalex.org/W606588608","https://openalex.org/W1507437630","https://openalex.org/W1550150926","https://openalex.org/W1575147392","https://openalex.org/W1991766321","https://openalex.org/W1993783307","https://openalex.org/W1997788271","https://openalex.org/W2019907360","https://openalex.org/W2023598261","https://openalex.org/W2049961932","https://openalex.org/W2056722718","https://openalex.org/W2065238451","https://openalex.org/W2066711129","https://openalex.org/W2068728923","https://openalex.org/W2080077270","https://openalex.org/W2193200384","https://openalex.org/W2225203892","https://openalex.org/W2242695251","https://openalex.org/W3039083618"],"related_works":["https://openalex.org/W2951180937","https://openalex.org/W2073579849","https://openalex.org/W1690719145","https://openalex.org/W2059208156","https://openalex.org/W2563462019","https://openalex.org/W4300197739","https://openalex.org/W2056088792","https://openalex.org/W2229973481","https://openalex.org/W2053002746","https://openalex.org/W2786782978"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,12,46,55,60,80,85,93,97,106],"spectrum":[3],"of":[4,15,30,35,62],"one-dimensional":[5],"periodic":[6],"lattices":[7],"with":[8],"geometric":[9,72],"interaction":[10],"in":[11,40,42],"asymptotic":[13,101],"regimes":[14],"vanishing":[16],"attenuation":[17],"and":[18,49,83,91,108],"long":[19],"lattice":[20],"lengths.":[21],"Our":[22],"mathematical":[23],"analysis":[24],"is":[25,77,111],"motivated":[26],"by":[27],"a":[28,63,71],"number":[29],"real-world":[31],"problems":[32],"where":[33],"chains":[34],"radiative":[36],"elements":[37,69],"are":[38,103],"embedded":[39],"waveguides":[41],"order":[43],"to":[44,58],"enhance":[45],"interlattice":[47],"interactions":[48],"collective":[50],"resonances.":[51],"Under":[52],"certain":[53],"assumptions":[54],"problem":[56],"reduces":[57],"determining":[59],"eigenvalues":[61,107],"complex-valued,":[64],"symmetric":[65],"Toeplitz":[66],"matrix":[67],"whose":[68],"follow":[70],"progression.":[73],"A":[74],"recurrence":[75],"formula":[76],"derived":[78,104],"for":[79,87,105],"characteristic":[81],"polynomial":[82],"becomes":[84],"basis":[86],"developing":[88],"spectral":[89],"asymptotics":[90],"resolving":[92],"eigenvalue":[94],"patterns":[95],"on":[96],"complex":[98],"plane.":[99],"Analytical":[100],"formulas":[102],"their":[109],"accuracy":[110],"assessed":[112],"numerically.":[113]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
