{"id":"https://openalex.org/W196561316","doi":null,"title":"Quantum Random Walks on the integer lattice via generating functions","display_name":"Quantum Random Walks on the integer lattice via generating functions","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W196561316","mag":"196561316"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.4647","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.4647","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.auckland.ac.nz/~mcw/Research/mvGF/asymultseq/Bressler-thesis.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5061958330","display_name":"Andrew Bressler","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andrew Bressler","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5061958330"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9487000107765198,"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"}},"topics":[{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9487000107765198,"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"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.01810000091791153,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.0044999998062849045,"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-walks","display_name":"quantum walks","score":0.9950000047683716},{"id":"https://openalex.org/keywords/nearest-neighbor-walks","display_name":"nearest-neighbor walks","score":0.718999981880188},{"id":"https://openalex.org/keywords/chirality","display_name":"chirality","score":0.7549999952316284},{"id":"https://openalex.org/keywords/multivariate-generating-functions","display_name":"multivariate generating functions","score":0.871999979019165},{"id":"https://openalex.org/keywords/polynomial-decay","display_name":"polynomial decay","score":0.7519999742507935},{"id":"https://openalex.org/keywords/exponential-decay","display_name":"exponential decay","score":0.9800000190734863},{"id":"https://openalex.org/keywords/bound-states","display_name":"bound states","score":0.8899999856948853},{"id":"https://openalex.org/keywords/asymptotic-wave-functions","display_name":"asymptotic wave functions","score":0.8500000238418579},{"id":"https://openalex.org/keywords/algebraic-varieties","display_name":"algebraic varieties","score":0.8130000233650208},{"id":"https://openalex.org/keywords/gaussian-curvature","display_name":"Gaussian curvature","score":0.7519999742507935},{"id":"https://openalex.org/keywords/integer-lattice","display_name":"integer lattice","score":0.4790000021457672}],"concepts":[{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.5516517758369446},{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.5461606979370117},{"id":"https://openalex.org/C142885752","wikidata":"https://www.wikidata.org/wiki/Q1252145","display_name":"Integer lattice","level":3,"score":0.5117011070251465},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5096518993377686},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4658285975456238},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4393949508666992},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43168923258781433},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42099031805992126},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.41126373410224915},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.39337682723999023},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3070255517959595},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.2601364552974701},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2592851519584656},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2460295557975769},{"id":"https://openalex.org/C56863137","wikidata":"https://www.wikidata.org/wiki/Q743139","display_name":"Half-integer","level":2,"score":0.21150493621826172},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12488293647766113},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.4647","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.4647","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.auckland.ac.nz/~mcw/Research/mvGF/asymultseq/Bressler-thesis.pdf","raw_type":"text"},{"id":"pmh:oai:repository.upenn.edu:dissertations-8705","doi":null,"is_oa":false,"landing_page_url":"https://repository.upenn.edu/dissertations/AAI3363259","pdf_url":null,"source":{"id":"https://openalex.org/S4377196331","display_name":"Scholarly Commons (University of Pennsylvania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I79576946","host_organization_name":"University of Pennsylvania","host_organization_lineage":["https://openalex.org/I79576946"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Dissertations available from ProQuest","raw_type":"text"},{"id":"mag:196561316","doi":null,"is_oa":false,"landing_page_url":"https://www.cs.auckland.ac.nz/~mcw/Research/mvGF/asymultseq/Bressler-thesis.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W196531003","https://openalex.org/W588295442","https://openalex.org/W1483218536","https://openalex.org/W1519689626","https://openalex.org/W1520302490","https://openalex.org/W1549451790","https://openalex.org/W1584610719","https://openalex.org/W1631356911","https://openalex.org/W1966092221","https://openalex.org/W1977415556","https://openalex.org/W1984066085","https://openalex.org/W1986225399","https://openalex.org/W1993202073","https://openalex.org/W2014057642","https://openalex.org/W2022080729","https://openalex.org/W2025956887","https://openalex.org/W2036172134","https://openalex.org/W2045254279","https://openalex.org/W2045390532","https://openalex.org/W2056390378","https://openalex.org/W2064321770","https://openalex.org/W2067639709","https://openalex.org/W2076252358","https://openalex.org/W2084652510","https://openalex.org/W2090733519","https://openalex.org/W2157395388","https://openalex.org/W2165264713","https://openalex.org/W2170706425","https://openalex.org/W2316271461","https://openalex.org/W2319466955","https://openalex.org/W2914659449","https://openalex.org/W3023478445","https://openalex.org/W3101846364"],"related_works":["https://openalex.org/W2076252358","https://openalex.org/W2307179729","https://openalex.org/W4394663235","https://openalex.org/W2019665760","https://openalex.org/W2942072042","https://openalex.org/W7096568378","https://openalex.org/W7099991504","https://openalex.org/W2098598610","https://openalex.org/W2303376821","https://openalex.org/W2887267797"],"abstract_inverted_index":{"We":[0,51,174,199],"analyze":[1],"several":[2],"families":[3],"of":[4,24,59,78,86,102,117,133,144,169,190,194],"one":[5],"and":[6,61,121],"two-dimensional":[7,126],"nearest":[8],"neighbor":[9],"Quantum":[10],"Random":[11],"Walks.":[12],"Using":[13],"a":[14,21,25,65,79,131,170,187],"multivariate":[15],"generating":[16],"function":[17,120],"analysis":[18],"we":[19,71,108,128,163],"give":[20],"simplified":[22],"proof":[23],"known":[26],"phenomenon":[27],"for":[28,112],"two-chirality":[29],"walks":[30,104,127,205],"on":[31,68,105],"the":[32,36,43,57,69,76,84,88,91,106,113,118,122,145,166,177,181,191,195],"line,":[33],"namely":[34],"that":[35],"walk":[37,67],"has":[38],"linear":[39],"speed":[40],"rather":[41],"than":[42],"diffusive":[44],"behavior":[45],"observed":[46],"in":[47,82,206],"classical":[48],"random":[49],"walks.":[50],"also":[52,175],"demonstrate":[53,72],"Airy":[54],"phenomena":[55],"between":[56],"regions":[58],"polynomial":[60,134],"exponential":[62],"decay.":[63],"For":[64,100],"three-chirality":[66],"line":[70,107],"similar":[73],"behavior,":[74],"with":[75,98,139,201],"addition":[77],"bound":[80],"state,":[81],"which":[83,136,162,184],"probability":[85,178],"finding":[87],"particle":[89],"at":[90],"origin":[92],"does":[93],"not":[94],"go":[95],"to":[96,157],"zero":[97],"time.":[99,140],"each":[101],"these":[103],"obtain":[109],"exact":[110],"formulae":[111],"leading":[114],"asymptotic":[115],"term":[116],"wave":[119],"location":[123],"probabilities.":[124],"Analyzing":[125],"again":[129],"find":[130],"region":[132,147,154],"decay":[135],"grows":[137],"linearly":[138],"The":[141,152],"limiting":[142],"shape":[143],"feasible":[146],"is,":[148],"however,":[149],"quite":[150],"different.":[151],"limit":[153,182],"turns":[155],"out":[156],"be":[158],"an":[159],"algebraic":[160,172,197],"set,":[161],"characterize":[164],"as":[165],"rational":[167],"image":[168],"compact":[171],"variety.":[173,198],"compute":[176],"profile":[179],"within":[180],"region,":[183],"is":[185],"essentially":[186],"negative":[188],"power":[189],"Gaussian":[192],"curvature":[193],"same":[196],"close":[200],"preliminary":[202],"work":[203],"concerning":[204],"higher":[207],"dimensions.":[208]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2016-06-24T00:00:00"}
