{"id":"https://openalex.org/W7221805992","doi":"https://doi.org/10.48550/arxiv.2610.18483","title":"Sign-indefinite transmission conditions and near-zero eigenvalues and resonances","display_name":"Sign-indefinite transmission conditions and near-zero eigenvalues and resonances","publication_year":2026,"publication_date":"2026-10-13","ids":{"openalex":"https://openalex.org/W7221805992","doi":"https://doi.org/10.48550/arxiv.2610.18483"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.18483","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.18483","pdf_url":"https://arxiv.org/pdf/2610.18483","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.18483","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066251692","display_name":"Andrea Mantile","orcid":"https://orcid.org/0000-0001-8619-0623","observed_orcids":["https://orcid.org/0000-0001-8619-0623"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mantile, Andrea","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5034542231","display_name":"Andrea Posilicano","orcid":"https://orcid.org/0000-0002-9273-1892","observed_orcids":["https://orcid.org/0000-0002-9273-1892"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Posilicano, Andrea","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9945999979972839,"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"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9945999979972839,"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/T10245","display_name":"Metamaterials and Metasurfaces Applications","score":0.0008999999845400453,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.000699999975040555,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metamaterials","display_name":"metamaterials","score":0.8190000057220459},{"id":"https://openalex.org/keywords/transmission-boundary-conditions","display_name":"transmission boundary conditions","score":0.8230000138282776},{"id":"https://openalex.org/keywords/resonance","display_name":"resonance","score":0.8159999847412109},{"id":"https://openalex.org/keywords/threshold-eigenvalues","display_name":"threshold eigenvalues","score":0.8709999918937683},{"id":"https://openalex.org/keywords/absolutely-continuous-spectrum","display_name":"absolutely continuous spectrum","score":0.7099999785423279},{"id":"https://openalex.org/keywords/point-spectrum","display_name":"point spectrum","score":0.8460000157356262},{"id":"https://openalex.org/keywords/neumann-poincare-operator","display_name":"Neumann-Poincar\u00e9 operator","score":0.9309999942779541},{"id":"https://openalex.org/keywords/analytic-perturbations","display_name":"analytic perturbations","score":0.7720000147819519},{"id":"https://openalex.org/keywords/negative-eigenvalues","display_name":"negative eigenvalues","score":0.7149999737739563}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8246999979019165},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6822999715805054},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6177999973297119},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6050999760627747},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5974000096321106},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.5839999914169312},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5299000144004822},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5264999866485596},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5013999938964844},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.49570000171661377},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4406999945640564},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.43299999833106995},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.38760000467300415},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.36649999022483826},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36000001430511475},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.33809998631477356},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.32170000672340393},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C46865736","wikidata":"https://www.wikidata.org/wiki/Q5348914","display_name":"Eigenvalue perturbation","level":3,"score":0.2581000030040741},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.257099986076355},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.2558000087738037}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.18483","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.18483","pdf_url":"https://arxiv.org/pdf/2610.18483","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.2610.18483","doi":"https://doi.org/10.48550/arxiv.2610.18483","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.18483","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.18483","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.18483","pdf_url":"https://arxiv.org/pdf/2610.18483","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221805992.pdf","grobid_xml":"https://content.openalex.org/works/W7221805992.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2087695870","https://openalex.org/W6996938416","https://openalex.org/W2313382249","https://openalex.org/W4410828395","https://openalex.org/W3111408347","https://openalex.org/W3121231554","https://openalex.org/W4401159353","https://openalex.org/W1589641165","https://openalex.org/W2738355165","https://openalex.org/W2764266422"],"abstract_inverted_index":{"We":[0,115],"consider":[1],"the":[2,14,27,47,58,71,85,95,113,120,123,128,132,136,138],"linear":[3],"operator":[4,134],"for":[5],"metamaterial":[6],"modeling":[7],"$$L_{c,d":[8],"}=(\u03c7_{\\RE^{3}\\backslash\\overline":[9],"\u03a9}+c)\\nabla\\!\\cdot":[10],"(\u03c7_{\\RE^{3}\\backslash\\overline":[11],"\u03a9}+d)\\nabla\\,,$$":[12],"where":[13],"material":[15],"parameters":[16,86],"$c>0$":[17],"and":[18,41,162],"$d$":[19,31],"are":[20],"constant":[21],"on":[22,34,84,119],"each":[23],"connected":[24],"component":[25,38],"of":[26,39,112,122,131,135,150,153,156,159,164],"bounded":[28],"domain":[29],"$\u03a9$,":[30],"is":[32,90,98],"negative":[33,160],"at":[35,46],"least":[36],"one":[37,157,163],"$\u03a9$":[40,97],"transmission":[42],"boundary":[43],"conditions":[44,83],"hold":[45],"interfaces.":[48],"It":[49],"turns":[50],"out":[51],"that":[52,88],"$L_{c,d":[53],"}$":[54],"has,":[55],"as":[56],"in":[57,79,146],"sign-definite":[59],"case,":[60],"an":[61],"absolutely":[62],"continuous":[63],"spectrum":[64],"equal":[65],"to":[66,70,127],"$[0,+\\infty)$;":[67],"however,":[68],"contrary":[69],"latter,":[72],"it":[73],"has":[74],"a":[75,91,104],"non-empty":[76],"point":[77],"spectrum;":[78],"particular,":[80],"we":[81,100],"find":[82],"so":[87],"zero":[89,139],"threshold":[92,105],"eigenvalue.":[93],"In":[94],"case":[96],"connected,":[99],"study":[101],"how":[102],"such":[103],"eigenvalue":[106,130,140],"behaves":[107],"under":[108],"$\\varepsilon$-small":[109],"analytic":[110],"perturbations":[111],"parameters.":[114],"show":[116],"that,":[117],"depending":[118],"position":[121],"number":[124],"$\\frac12\\,\\frac{1+d(\\ve)}{1-d(\\ve)}$":[125],"relative":[126],"nearest":[129],"Neumann-Poincar\u00e9":[133],"interface,":[137],"splits":[141],"into":[142],"two":[143,151],"branches":[144,152],"(analytic":[145],"$\\varepsilon^{1/2}$),":[147],"consisting":[148],"either":[149],"resonances,":[154],"or":[155],"branch":[158],"eigenvalues":[161],"resonances.":[165]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-15T00:00:00"}
