{"id":"https://openalex.org/W7215909386","doi":"https://doi.org/10.48550/arxiv.2610.01844","title":"Ballistic Speed and Potential-Theoretic Recurrence for Homogeneous Open Quantum Random Walks","display_name":"Ballistic Speed and Potential-Theoretic Recurrence for Homogeneous Open Quantum Random Walks","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7215909386","doi":"https://doi.org/10.48550/arxiv.2610.01844"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.01844","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01844","pdf_url":"https://arxiv.org/pdf/2610.01844","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.01844","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033552413","display_name":"Ameur Dhahri","orcid":"https://orcid.org/0000-0003-0580-7025","observed_orcids":["https://orcid.org/0000-0003-0580-7025"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dhahri, Ameur","raw_affiliation_strings":["Department of Applied Mathematics and"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5155371359","display_name":"Chul Ki Ko","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ko, Chul Ki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028799450","display_name":"Mukhamedov Farrukh","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I119060216","display_name":"Hankyong National University","ror":"https://ror.org/0031nsg68","country_code":"KR","type":"education","lineage":["https://openalex.org/I119060216"]},{"id":"https://openalex.org/I201726411","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862","country_code":"AE","type":"education","lineage":["https://openalex.org/I201726411"]}],"countries":["AE","KR"],"is_corresponding":false,"raw_author_name":"Mukhamedov, Farrukh","raw_affiliation_strings":["Department of Mathematical Sciences , United Arab Emirates University , P.O. Box No. 15551 , Al Ain , Abu Dhabi , United Arab Emirates","Institute for Integrated Mathematical Sciences , Hankyong National University , 327 Jungang-ro , Anseong-si , Gyeonggi-do 17579 , Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , United Arab Emirates University , P.O. Box No. 15551 , Al Ain , Abu Dhabi , United Arab Emirates","institution_ids":["https://openalex.org/I201726411"]},{"raw_affiliation_string":"Institute for Integrated Mathematical Sciences , Hankyong National University , 327 Jungang-ro , Anseong-si , Gyeonggi-do 17579 , Korea","institution_ids":["https://openalex.org/I119060216"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026843134","display_name":"Hyun Jae Yoo","orcid":"https://orcid.org/0000-0003-0683-2898","observed_orcids":["https://orcid.org/0000-0003-0683-2898"]},"institutions":[{"id":"https://openalex.org/I201726411","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862","country_code":"AE","type":"education","lineage":["https://openalex.org/I201726411"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Yoo, Hyun Jae","raw_affiliation_strings":["Department of Mathematical Sciences , United Arab Emirates University , P.O. Box No. 15551 , Al Ain , Abu Dhabi , United Arab Emirates"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , United Arab Emirates University , P.O. Box No. 15551 , Al Ain , Abu Dhabi , United Arab Emirates","institution_ids":["https://openalex.org/I201726411"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.5468999743461609,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.5468999743461609,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.09709999710321426,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.09189999848604202,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ballistic-transport","display_name":"ballistic transport","score":0.7310000061988831},{"id":"https://openalex.org/keywords/recurrence","display_name":"recurrence","score":0.703000009059906},{"id":"https://openalex.org/keywords/transience","display_name":"transience","score":0.847000002861023},{"id":"https://openalex.org/keywords/potential-kernel","display_name":"potential kernel","score":0.8349999785423279},{"id":"https://openalex.org/keywords/absorption","display_name":"absorption","score":0.4050000011920929},{"id":"https://openalex.org/keywords/drift","display_name":"drift","score":0.37700000405311584}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.676800012588501},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.6466000080108643},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5983999967575073},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5468999743461609},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4830000102519989},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4652000069618225},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4284999966621399},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.4275999963283539},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.4081000089645386},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4056999981403351},{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.4036000072956085},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.39430001378059387},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.39100000262260437},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.3840999901294708},{"id":"https://openalex.org/C192683347","wikidata":"https://www.wikidata.org/wiki/Q4851798","display_name":"Ballistic conduction","level":3,"score":0.3682999908924103},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.35989999771118164},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.3571999967098236},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3206000030040741},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.30399999022483826},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.2992999851703644},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2533999979496002}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.01844","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01844","pdf_url":"https://arxiv.org/pdf/2610.01844","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.2610.01844","doi":"https://doi.org/10.48550/arxiv.2610.01844","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.01844","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-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.01844","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01844","pdf_url":"https://arxiv.org/pdf/2610.01844","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":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320328359","display_name":"Ministry of Science and ICT, South Korea","ror":"https://ror.org/01wpjm123"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7215909386.pdf","grobid_xml":"https://content.openalex.org/works/W7215909386.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2056390378","https://openalex.org/W2059551605","https://openalex.org/W2077461478","https://openalex.org/W2156029098","https://openalex.org/W3105964729","https://openalex.org/W4403369782"],"related_works":["https://openalex.org/W7097959567","https://openalex.org/W3128751782","https://openalex.org/W7099367768","https://openalex.org/W438687894","https://openalex.org/W2089483581","https://openalex.org/W6996129732","https://openalex.org/W7033765609","https://openalex.org/W3105964729","https://openalex.org/W2912034194","https://openalex.org/W3182880319"],"abstract_inverted_index":{"Our":[0],"study":[1],"connects":[2],"root-mean-square":[3],"ballistic":[4,85],"transport":[5],"to":[6,80,134],"potential-theoretic":[7],"recurrence":[8,116],"for":[9,54,197],"finite-range":[10],"open":[11],"quantum":[12],"random":[13],"walks.":[14],"In":[15],"homogeneous":[16],"walks":[17,97],"with":[18],"primitive":[19],"local":[20,45],"channels,":[21],"finitely":[22],"many":[23],"simple":[24],"periodic":[25,43],"Fourier":[26,32],"peripheral":[27],"eigenvalues,":[28],"no":[29],"nonzero":[30,55,91],"stationary":[31],"mode,":[33],"and":[34,48,76,95,104,180,188,200],"a":[35,42,115,138,193],"nondegenerate":[36],"quadratic":[37],"spectral":[38,175],"term,":[39],"we":[40],"prove":[41],"uniform":[44],"limit":[46],"theorem":[47],"recover":[49],"exponential":[50],"finite-set":[51],"return":[52,166],"bounds":[53],"drift.":[56],"The":[57,111,145],"centered":[58,96,169],"case":[59],"yields":[60],"strong":[61],"Green-function":[62],"asymptotics":[63,73],"in":[64,74,100,108,121,177],"at":[65],"least":[66],"three":[67],"dimensions,":[68],"as":[69,71],"well":[70],"potential-kernel":[72],"one":[75,103],"two":[77,105],"dimensions.":[78,110],"According":[79],"these":[81],"assumptions,":[82],"the":[83,88,118,150,158,173],"RMS":[84,147],"speed":[86,148,199],"equals":[87],"drift":[89,92],"norm,":[90],"indicates":[93],"transience,":[94],"are":[98],"recurring":[99],"effective":[101],"dimensions":[102,179],"but":[106,157],"transitory":[107],"higher":[109],"low-dimensional":[112],"finding":[113],"shows":[114],"of":[117,141,153],"origin":[119],"projection":[120],"TOM.":[122],"For":[123],"reducible":[124],"walks,":[125],"an":[126,135],"explicit":[127,182],"harmonic":[128],"\\(h\\)-transform":[129],"converts":[130],"each":[131],"absorption":[132],"component":[133,155,165],"OQRW,":[136],"providing":[137],"detailed":[139],"breakdown":[140],"Green":[142],"occupation":[143],"potentials.":[144],"squared":[146,154],"is":[149],"absorption-weighted":[151],"mean":[152],"drifts,":[156],"reduced":[159],"drift-dimension":[160],"classification":[161],"also":[162],"needs":[163],"specific":[164],"estimations.":[167],"A":[168],"noncommuting":[170],"family":[171],"validates":[172],"fundamental":[174],"assumptions":[176],"all":[178],"provides":[181],"potential":[183],"constants.":[184],"Exact":[185],"finite":[186],"traps":[187],"sparse":[189],"reflecting":[190],"barriers":[191],"provide":[192],"complementary":[194],"nonhomogeneous":[195],"method":[196],"zero":[198],"TOM":[201],"recurrence.":[202]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}
