{"id":"https://openalex.org/W2605918320","doi":"https://doi.org/10.3390/e19040164","title":"Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems","display_name":"Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems","publication_year":2017,"publication_date":"2017-04-09","ids":{"openalex":"https://openalex.org/W2605918320","doi":"https://doi.org/10.3390/e19040164","mag":"2605918320"},"language":"en","primary_location":{"id":"doi:10.3390/e19040164","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19040164","pdf_url":"https://www.mdpi.com/1099-4300/19/4/164/pdf?version=1491906160","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/19/4/164/pdf?version=1491906160","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079767345","display_name":"David Puertas\u2010Centeno","orcid":"https://orcid.org/0000-0002-3189-7733"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"David Puertas-Centeno","raw_affiliation_strings":["Departamento de F\u00edsica At\u00f3mica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain","Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Universidad de Granada, 18071-Granada, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica At\u00f3mica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Universidad de Granada, 18071-Granada, Spain","institution_ids":["https://openalex.org/I173304897"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041737989","display_name":"I. V. Toranzo","orcid":null},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Irene Toranzo","raw_affiliation_strings":["Departamento de F\u00edsica At\u00f3mica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain","Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Universidad de Granada, 18071-Granada, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica At\u00f3mica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Universidad de Granada, 18071-Granada, Spain","institution_ids":["https://openalex.org/I173304897"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010176735","display_name":"J. S. Dehesa","orcid":"https://orcid.org/0000-0003-4397-9426"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Jes\u00fas Dehesa","raw_affiliation_strings":["Departamento de F\u00edsica At\u00f3mica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain","Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Universidad de Granada, 18071-Granada, Spain"],"raw_orcid":"https://orcid.org/0000-0003-4397-9426","affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica At\u00f3mica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Universidad de Granada, 18071-Granada, Spain","institution_ids":["https://openalex.org/I173304897"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010176735"],"corresponding_institution_ids":["https://openalex.org/I173304897"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":1.7893,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.8526663,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"19","issue":"4","first_page":"164","last_page":"164"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9300000071525574,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9286999702453613,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/entropic-uncertainty","display_name":"Entropic uncertainty","score":0.6991186141967773},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5974124670028687},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.517630398273468},{"id":"https://openalex.org/keywords/uncertainty-principle","display_name":"Uncertainty principle","score":0.4562905430793762},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.41949281096458435},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3384838104248047},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3365141749382019},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.22140595316886902}],"concepts":[{"id":"https://openalex.org/C37731324","wikidata":"https://www.wikidata.org/wiki/Q5380783","display_name":"Entropic uncertainty","level":4,"score":0.6991186141967773},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5974124670028687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.517630398273468},{"id":"https://openalex.org/C181543814","wikidata":"https://www.wikidata.org/wiki/Q44746","display_name":"Uncertainty principle","level":3,"score":0.4562905430793762},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.41949281096458435},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3384838104248047},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3365141749382019},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.22140595316886902},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e19040164","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19040164","pdf_url":"https://www.mdpi.com/1099-4300/19/4/164/pdf?version=1491906160","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1704.03677","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1704.03677","pdf_url":"https://arxiv.org/pdf/1704.03677","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,"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":"pmh:oai:digibug.ugr.es:10481/49123","is_oa":false,"landing_page_url":"http://hdl.handle.net/10481/49123","pdf_url":null,"source":{"id":"https://openalex.org/S4306400567","display_name":"Institutional Repository of the University of Granada (University of Granada)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I173304897","host_organization_name":"Universidad de Granada","host_organization_lineage":["https://openalex.org/I173304897"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:eciencia.urjc.es:10115/40181","is_oa":true,"landing_page_url":"https://hdl.handle.net/10115/40181","pdf_url":null,"source":{"id":"https://openalex.org/S4377196484","display_name":"BURJC Digital (King Juan Carlos University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I182083151","host_organization_name":"Universidad Rey Juan Carlos","host_organization_lineage":["https://openalex.org/I182083151"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:mdpi.com:/1099-4300/19/4/164/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e19040164","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":"Entropy; Volume 19; Issue 4; Pages: 164","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e19040164","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19040164","pdf_url":"https://www.mdpi.com/1099-4300/19/4/164/pdf?version=1491906160","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G315291018","display_name":null,"funder_award_id":"FIS2014- 54497P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G3270993484","display_name":null,"funder_award_id":"FIS2014-59311P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G4881254354","display_name":null,"funder_award_id":"FQM-207","funder_id":"https://openalex.org/F4320326754","funder_display_name":"Junta de Andaluc\u00eda"},{"id":"https://openalex.org/G6763015805","display_name":null,"funder_award_id":"FQM-7276","funder_id":"https://openalex.org/F4320326754","funder_display_name":"Junta de Andaluc\u00eda"}],"funders":[{"id":"https://openalex.org/F4320321764","display_name":"Ministerio de Educaci\u00f3n, Cultura y Deporte","ror":"https://ror.org/03nc27g21"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320326754","display_name":"Junta de Andaluc\u00eda","ror":"https://ror.org/01jem9c82"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":108,"referenced_works":["https://openalex.org/W187081158","https://openalex.org/W425208196","https://openalex.org/W575495179","https://openalex.org/W587044833","https://openalex.org/W590791627","https://openalex.org/W632639409","https://openalex.org/W637154592","https://openalex.org/W1462309304","https://openalex.org/W1509489218","https://openalex.org/W1556174842","https://openalex.org/W1593125407","https://openalex.org/W1670395052","https://openalex.org/W1805665308","https://openalex.org/W1967451242","https://openalex.org/W1973343588","https://openalex.org/W1975584024","https://openalex.org/W1981050900","https://openalex.org/W1981744268","https://openalex.org/W1983346172","https://openalex.org/W1983874169","https://openalex.org/W1989330584","https://openalex.org/W1989958779","https://openalex.org/W1995785082","https://openalex.org/W1995875735","https://openalex.org/W1996978411","https://openalex.org/W1998950815","https://openalex.org/W2001885186","https://openalex.org/W2007211596","https://openalex.org/W2012708878","https://openalex.org/W2013564845","https://openalex.org/W2019426410","https://openalex.org/W2022230522","https://openalex.org/W2022418146","https://openalex.org/W2028733879","https://openalex.org/W2030940862","https://openalex.org/W2035245840","https://openalex.org/W2038060808","https://openalex.org/W2044327259","https://openalex.org/W2044463665","https://openalex.org/W2046181715","https://openalex.org/W2049551726","https://openalex.org/W2069622131","https://openalex.org/W2071647555","https://openalex.org/W2073797119","https://openalex.org/W2073814871","https://openalex.org/W2073991973","https://openalex.org/W2074494525","https://openalex.org/W2075835929","https://openalex.org/W2076795554","https://openalex.org/W2080522629","https://openalex.org/W2081658913","https://openalex.org/W2082118878","https://openalex.org/W2087663371","https://openalex.org/W2087910039","https://openalex.org/W2088325035","https://openalex.org/W2089525630","https://openalex.org/W2090542924","https://openalex.org/W2091271713","https://openalex.org/W2092108225","https://openalex.org/W2094654291","https://openalex.org/W2096960957","https://openalex.org/W2103478788","https://openalex.org/W2105264387","https://openalex.org/W2117675594","https://openalex.org/W2118932052","https://openalex.org/W2119103347","https://openalex.org/W2122882636","https://openalex.org/W2124498007","https://openalex.org/W2127334651","https://openalex.org/W2135385767","https://openalex.org/W2140024018","https://openalex.org/W2151149485","https://openalex.org/W2156430242","https://openalex.org/W2158852798","https://openalex.org/W2159410513","https://openalex.org/W2235249560","https://openalex.org/W2286309935","https://openalex.org/W2305548949","https://openalex.org/W2336263576","https://openalex.org/W2409978206","https://openalex.org/W2517820385","https://openalex.org/W2520506708","https://openalex.org/W2561886951","https://openalex.org/W2582309436","https://openalex.org/W2611097588","https://openalex.org/W2757870058","https://openalex.org/W2949868881","https://openalex.org/W2951838449","https://openalex.org/W2951886102","https://openalex.org/W2993383518","https://openalex.org/W3098781922","https://openalex.org/W3098895776","https://openalex.org/W3100833629","https://openalex.org/W3102465934","https://openalex.org/W3102855270","https://openalex.org/W3103436189","https://openalex.org/W3103782918","https://openalex.org/W3103850736","https://openalex.org/W3105442285","https://openalex.org/W3105729759","https://openalex.org/W3123888769","https://openalex.org/W3208358767","https://openalex.org/W4234562827","https://openalex.org/W4243963569","https://openalex.org/W6644063693","https://openalex.org/W6645467904","https://openalex.org/W6658343886","https://openalex.org/W6812297037"],"related_works":["https://openalex.org/W2187423525","https://openalex.org/W2121796026","https://openalex.org/W3093147984","https://openalex.org/W2736047337","https://openalex.org/W3018450082","https://openalex.org/W2950765180","https://openalex.org/W2605918320","https://openalex.org/W3088184943","https://openalex.org/W2077059494","https://openalex.org/W2995917597"],"abstract_inverted_index":{"The":[0,68],"D-dimensional":[1,110],"harmonic":[2,111],"system":[3,49],"(i.e.,":[4],"a":[5,12],"particle":[6],"moving":[7],"under":[8],"the":[9,18,21,25,37,41,53,58,63,80,87,99,109,115,124,127,131,135,140],"action":[10],"of":[11,24,27,40,47,65,108,139],"quadratic":[13],"potential)":[14],"is,":[15],"together":[16],"with":[17],"hydrogenic":[19,132],"system,":[20],"main":[22],"prototype":[23],"physics":[26],"multidimensional":[28,70],"quantum":[29],"systems.":[30],"In":[31],"this":[32,48],"work,":[33],"we":[34],"rigorously":[35],"determine":[36],"leading":[38],"term":[39],"Heisenberg-like":[42,100],"and":[43,57,93,101,142],"entropy-like":[44],"uncertainty":[45,72,89,104],"measures":[46],"as":[50,126],"given":[51],"by":[52],"radial":[54],"expectation":[55],"values":[56],"R\u00e9nyi":[59],"entropies,":[60],"respectively,":[61],"at":[62],"limit":[64,122],"large":[66],"D.":[67],"associated":[69],"position-momentum":[71],"relations":[73,105],"are":[74,123],"discussed,":[75],"showing":[76],"that":[77],"they":[78],"saturate":[79],"corresponding":[81,128],"general":[82],"ones.":[83],"A":[84],"conjecture":[85],"about":[86],"Shannon-like":[88],"relation":[90],"is":[91,97],"given,":[92],"an":[94],"interesting":[95],"phenomenon":[96],"observed:":[98],"R\u00e9nyi-entropy-based":[102],"equality-type":[103],"for":[106,130],"all":[107],"oscillator":[112,141],"states":[113],"in":[114],"pseudoclassical":[116],"(":[117],"D":[118],"\u2192":[119],"\u221e":[120],")":[121],"same":[125],"ones":[129],"systems,":[133],"despite":[134],"so":[136],"different":[137],"character":[138],"Coulomb":[143],"potentials.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
