{"id":"https://openalex.org/W7204671234","doi":"https://doi.org/10.48550/arxiv.2608.27326","title":"Arbitrarily Fast Quantum Dispersion in Long-Range Crystals","display_name":"Arbitrarily Fast Quantum Dispersion in Long-Range Crystals","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204671234","doi":"https://doi.org/10.48550/arxiv.2608.27326"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.27326","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27326","pdf_url":"https://arxiv.org/pdf/2608.27326","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.27326","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003741582","display_name":"Ga\u00e9tan Leclerc","orcid":"https://orcid.org/0000-0001-9424-6420","observed_orcids":["https://orcid.org/0000-0001-9424-6420"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leclerc, Ga\u00e9tan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019652483","display_name":"Mostafa Sabri","orcid":"https://orcid.org/0000-0002-6857-652X","observed_orcids":["https://orcid.org/0000-0002-6857-652X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sabri, Mostafa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5022780659","display_name":"Tuomas Sahlsten","orcid":"https://orcid.org/0000-0001-5625-5481","observed_orcids":["https://orcid.org/0000-0001-5625-5481"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sahlsten, Tuomas","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":2,"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":0.8651999831199646,"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":0.8651999831199646,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.05260000005364418,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.03739999979734421,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-dispersion","display_name":"quantum dispersion","score":0.6349999904632568},{"id":"https://openalex.org/keywords/one-dimensional-crystals","display_name":"one-dimensional crystals","score":0.6499999761581421},{"id":"https://openalex.org/keywords/weierstrass-function","display_name":"Weierstrass function","score":0.9430000185966492},{"id":"https://openalex.org/keywords/fourier-decay","display_name":"Fourier decay","score":0.7390000224113464},{"id":"https://openalex.org/keywords/transfer-operator","display_name":"transfer operator","score":0.7799999713897705},{"id":"https://openalex.org/keywords/van-der-corput-lemma","display_name":"van der Corput lemma","score":0.8759999871253967},{"id":"https://openalex.org/keywords/local-time","display_name":"local time","score":0.8320000171661377},{"id":"https://openalex.org/keywords/floquet-hamiltonian","display_name":"Floquet Hamiltonian","score":0.6129999756813049}],"concepts":[{"id":"https://openalex.org/C136534824","wikidata":"https://www.wikidata.org/wiki/Q2771020","display_name":"Lacunarity","level":4,"score":0.6022999882698059},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5677000284194946},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5257999897003174},{"id":"https://openalex.org/C2777952282","wikidata":"https://www.wikidata.org/wiki/Q3354606","display_name":"Transfer operator","level":2,"score":0.49720001220703125},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.49459999799728394},{"id":"https://openalex.org/C55649039","wikidata":"https://www.wikidata.org/wiki/Q902618","display_name":"Floquet theory","level":3,"score":0.47029998898506165},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4666999876499176},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.4438000023365021},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4187999963760376},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41760000586509705},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.40689998865127563},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.3921000063419342},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.390500009059906},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.3431999981403351},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32499998807907104},{"id":"https://openalex.org/C2776175482","wikidata":"https://www.wikidata.org/wiki/Q1195816","display_name":"Transfer (computing)","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3021000027656555},{"id":"https://openalex.org/C2992576796","wikidata":"https://www.wikidata.org/wiki/Q1171303","display_name":"Quantum particle","level":3,"score":0.2964000105857849},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C65945562","wikidata":"https://www.wikidata.org/wiki/Q3075283","display_name":"Weierstrass functions","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2630000114440918},{"id":"https://openalex.org/C122890649","wikidata":"https://www.wikidata.org/wiki/Q7834016","display_name":"Transfer matrix","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.259799987077713},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.27326","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27326","pdf_url":"https://arxiv.org/pdf/2608.27326","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.27326","doi":"https://doi.org/10.48550/arxiv.2608.27326","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.27326","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:2608.27326","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27326","pdf_url":"https://arxiv.org/pdf/2608.27326","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":"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/W7204671234.pdf","grobid_xml":"https://content.openalex.org/works/W7204671234.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W3179677864","https://openalex.org/W4379473692","https://openalex.org/W4379473961","https://openalex.org/W4385003450","https://openalex.org/W4388514831","https://openalex.org/W4403771344","https://openalex.org/W4414921892","https://openalex.org/W4415023999","https://openalex.org/W4416841407","https://openalex.org/W6910405299","https://openalex.org/W6948290029","https://openalex.org/W7163998804","https://openalex.org/W7169830389","https://openalex.org/W7171353057"],"related_works":["https://openalex.org/W2252727461","https://openalex.org/W3088229197","https://openalex.org/W7052721112","https://openalex.org/W2023321571","https://openalex.org/W4390571390","https://openalex.org/W2582495708","https://openalex.org/W4399290950","https://openalex.org/W2205594765","https://openalex.org/W7167581877","https://openalex.org/W4411250156"],"abstract_inverted_index":{"We":[0],"construct":[1],"the":[2,31,46,69],"first":[3],"examples":[4],"of":[5,18,45,72,76],"one-dimensional":[6],"long-range":[7],"crystals":[8],"exhibiting":[9],"arbitrarily":[10],"fast":[11,32],"polynomial":[12],"dispersive":[13],"bounds.":[14],"The":[15,34],"Floquet":[16],"functions":[17,75],"our":[19],"Hamiltonians":[20],"are":[21],"highly":[22],"oscillatory":[23],"Weierstrass":[24,64,74],"functions,":[25],"whose":[26],"rough":[27],"autosimilar":[28],"structure":[29],"drives":[30],"dispersion.":[33],"proof":[35],"develops":[36],"a":[37,51,58,67,85],"new":[38],"Fourier":[39],"decay":[40],"theory":[41],"for":[42,63],"$C^\u03b1$":[43],"images":[44],"Lebesgue":[47],"measure,":[48],"based":[49],"on":[50],"Dolgopyat-inspired":[52],"transfer":[53],"operator":[54],"method,":[55],"and":[56,81,90],"yields":[57],"van":[59],"der":[60],"Corput":[61],"lemma":[62],"functions.":[65],"As":[66],"consequence,":[68],"local":[70],"time":[71],"classical":[73],"sufficiently":[77],"large":[78],"lacunarity":[79],"exists":[80],"is":[82],"$C^k$,":[83],"answering":[84],"question":[86],"raised":[87],"by":[88],"Geman":[89],"Horowitz":[91],"in":[92],"1980.":[93]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-30T00:00:00"}
