{"id":"https://openalex.org/W3127130960","doi":"https://doi.org/10.3390/sym13020306","title":"A Quantum Time Coordinate","display_name":"A Quantum Time Coordinate","publication_year":2021,"publication_date":"2021-02-11","ids":{"openalex":"https://openalex.org/W3127130960","doi":"https://doi.org/10.3390/sym13020306","mag":"3127130960"},"language":"en","primary_location":{"id":"doi:10.3390/sym13020306","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13020306","pdf_url":"https://www.mdpi.com/2073-8994/13/2/306/pdf?version=1614142118","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/2/306/pdf?version=1614142118","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026289651","display_name":"Armando Mart\u00ednez-P\u00e9rez","orcid":"https://orcid.org/0000-0002-8380-5888"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Armando Mart\u00ednez-P\u00e9rez","raw_affiliation_strings":["Departamento de F\u00edsica, Cinvestav, Ciudad de Mexico 07300, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-8380-5888","affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Cinvestav, Ciudad de Mexico 07300, Mexico","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039792825","display_name":"Gabino Torres-Vega","orcid":"https://orcid.org/0000-0002-3122-0546"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Gabino Torres-Vega","raw_affiliation_strings":["Departamento de F\u00edsica, Cinvestav, Ciudad de Mexico 07300, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-3122-0546","affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Cinvestav, Ciudad de Mexico 07300, Mexico","institution_ids":["https://openalex.org/I68368234"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039792825"],"corresponding_institution_ids":["https://openalex.org/I68368234"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1399,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.51897168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"13","issue":"2","first_page":"306","last_page":"306"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9993000030517578,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9993000030517578,"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/T10382","display_name":"Quantum and electron transport phenomena","score":0.9988999962806702,"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":0.9984999895095825,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7929655313491821},{"id":"https://openalex.org/keywords/coordinate-system","display_name":"Coordinate system","score":0.582973837852478},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5663192868232727},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5641700029373169},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4923902750015259},{"id":"https://openalex.org/keywords/quantum-system","display_name":"Quantum system","score":0.4639202356338501},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4378969669342041},{"id":"https://openalex.org/keywords/particle-in-a-box","display_name":"Particle in a box","score":0.4116226136684418},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.34846001863479614},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.33715301752090454},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2363821268081665},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13570216298103333}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7929655313491821},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.582973837852478},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5663192868232727},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5641700029373169},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4923902750015259},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.4639202356338501},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4378969669342041},{"id":"https://openalex.org/C197806323","wikidata":"https://www.wikidata.org/wiki/Q909221","display_name":"Particle in a box","level":3,"score":0.4116226136684418},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.34846001863479614},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.33715301752090454},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2363821268081665},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13570216298103333},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13020306","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13020306","pdf_url":"https://www.mdpi.com/2073-8994/13/2/306/pdf?version=1614142118","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:48c2076a50a54d0d996ac5f33656fd35","is_oa":true,"landing_page_url":"https://doaj.org/article/48c2076a50a54d0d996ac5f33656fd35","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 2, p 306 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/2/306/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13020306","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Symmetry; Volume 13; Issue 2; Pages: 306","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13020306","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13020306","pdf_url":"https://www.mdpi.com/2073-8994/13/2/306/pdf?version=1614142118","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8700000047683716}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3127130960.pdf","grobid_xml":"https://content.openalex.org/works/W3127130960.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W8994522","https://openalex.org/W119038370","https://openalex.org/W603207913","https://openalex.org/W617296069","https://openalex.org/W1509732379","https://openalex.org/W1510159182","https://openalex.org/W1662373048","https://openalex.org/W1982461707","https://openalex.org/W1996432345","https://openalex.org/W2001133031","https://openalex.org/W2008843935","https://openalex.org/W2014131253","https://openalex.org/W2019442644","https://openalex.org/W2020050358","https://openalex.org/W2024125882","https://openalex.org/W2041174349","https://openalex.org/W2045547010","https://openalex.org/W2047749712","https://openalex.org/W2087435909","https://openalex.org/W2094456552","https://openalex.org/W2103504195","https://openalex.org/W2105057160","https://openalex.org/W2137546069","https://openalex.org/W2165906163","https://openalex.org/W2173524688","https://openalex.org/W2187134934","https://openalex.org/W2262991546","https://openalex.org/W2317065091","https://openalex.org/W2489617394","https://openalex.org/W2595505940","https://openalex.org/W2762531928","https://openalex.org/W2791747373","https://openalex.org/W2985141412","https://openalex.org/W3014293911","https://openalex.org/W3103550728","https://openalex.org/W3120934736","https://openalex.org/W4254425416","https://openalex.org/W4300489453","https://openalex.org/W6687023078"],"related_works":["https://openalex.org/W2165749285","https://openalex.org/W2062626603","https://openalex.org/W3012161390","https://openalex.org/W2474979212","https://openalex.org/W2562455930","https://openalex.org/W2001036795","https://openalex.org/W2384394297","https://openalex.org/W2060813082","https://openalex.org/W2995995356","https://openalex.org/W4312206220"],"abstract_inverted_index":{"We":[0,65],"discuss":[1],"quantum":[2],"time":[3,19,22,31,40,44,92],"states":[4,23],"formed":[5],"with":[6,13],"a":[7,18,83,87,97],"finite":[8],"number":[9],"of":[10,16,26,38,61,71],"energy":[11],"eigenstates":[12,25,41,93],"the":[14,27,58,62,68,72,75,80],"purpose":[15],"obtaining":[17],"coordinate.":[20],"These":[21],"are":[24],"recently":[28],"introduced":[29],"discrete":[30],"operator.":[32],"The":[33],"coordinate":[34,98],"and":[35,46],"momentum":[36],"representations":[37],"these":[39],"resemble":[42],"classical":[43,48],"curves":[45],"become":[47],"at":[49],"high":[50],"energies.":[51],"To":[52],"illustrate":[53],"this":[54],"behavior,":[55],"we":[56,85],"consider":[57],"simple":[59],"example":[60],"particle-in-a-box":[63],"model.":[64],"can":[66],"follow":[67],"quantum-classical":[69],"transition":[70],"system.":[73,99],"Among":[74],"many":[76],"existing":[77],"solutions":[78],"for":[79,94],"particle":[81],"in":[82],"box,":[84],"use":[86,95],"set":[88],"which":[89],"leads":[90],"to":[91],"as":[96]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2021-02-15T00:00:00"}