Entropic Analysis of the Quantum Oscillator with a Minimal Length

Autores
Puertas Centeno, David; Portesi, Mariela Adelina
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The well-known Heisenberg-Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system. Different modified commutation relations have been considered in the last years with the purpose of taking into account the effect of quantum gravity. Indeed it can be seen that letting [X,P]=iℏ(1+β P^2) implies the existence of a minimal length proportional to sqrt(β). The Bialynicki-Birula-Mycielski entropic uncertainty relation in terms of Shannon entropies is also seen to be deformed in the presence of a minimal length, corresponding to a strictly positive deformation parameter β. Generalized entropies can be implemented. Indeed, results for the sum of position and (auxiliary) momentum Rényi entropies with conjugated indices have been provided recently for the ground and first excited state. We present numerical findings for conjugated pairs of entropic indices, for the lowest lying levels of the deformed harmonic oscillator system in 1D, taking into account the position distribution for the wavefunction and the actual momentum.
Fil: Puertas Centeno, David. Universidad Rey Juan Carlos; España
Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Materia
UNCERTAINTY RELATIONS
INFORMATION ENTROPY
QUANTUM GRAVITY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/128839
Acceder
id CONICETDig_8066f25eefe9ce1c6ca7c986fee5bb5f
oai_identifier_str oai:ri.conicet.gov.ar:11336/128839
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Entropic Analysis of the Quantum Oscillator with a Minimal LengthPuertas Centeno, DavidPortesi, Mariela AdelinaUNCERTAINTY RELATIONSINFORMATION ENTROPYQUANTUM GRAVITYhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The well-known Heisenberg-Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system. Different modified commutation relations have been considered in the last years with the purpose of taking into account the effect of quantum gravity. Indeed it can be seen that letting [X,P]=iℏ(1+β P^2) implies the existence of a minimal length proportional to sqrt(β). The Bialynicki-Birula-Mycielski entropic uncertainty relation in terms of Shannon entropies is also seen to be deformed in the presence of a minimal length, corresponding to a strictly positive deformation parameter β. Generalized entropies can be implemented. Indeed, results for the sum of position and (auxiliary) momentum Rényi entropies with conjugated indices have been provided recently for the ground and first excited state. We present numerical findings for conjugated pairs of entropic indices, for the lowest lying levels of the deformed harmonic oscillator system in 1D, taking into account the position distribution for the wavefunction and the actual momentum.Fil: Puertas Centeno, David. Universidad Rey Juan Carlos; EspañaFil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaMultidisciplinary Digital Publishing Institute2019-11-19info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/128839Puertas Centeno, David; Portesi, Mariela Adelina; Entropic Analysis of the Quantum Oscillator with a Minimal Length; Multidisciplinary Digital Publishing Institute; Proceedings; 12; 1; 19-11-2019; 1-42504-3900CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/2504-3900/12/1/57info:eu-repo/semantics/altIdentifier/doi/10.3390/proceedings2019012057info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:16:52Zoai:ri.conicet.gov.ar:11336/128839instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:16:52.409CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Entropic Analysis of the Quantum Oscillator with a Minimal Length
title Entropic Analysis of the Quantum Oscillator with a Minimal Length
spellingShingle Entropic Analysis of the Quantum Oscillator with a Minimal Length
Puertas Centeno, David
UNCERTAINTY RELATIONS
INFORMATION ENTROPY
QUANTUM GRAVITY
title_short Entropic Analysis of the Quantum Oscillator with a Minimal Length
title_full Entropic Analysis of the Quantum Oscillator with a Minimal Length
title_fullStr Entropic Analysis of the Quantum Oscillator with a Minimal Length
title_full_unstemmed Entropic Analysis of the Quantum Oscillator with a Minimal Length
title_sort Entropic Analysis of the Quantum Oscillator with a Minimal Length
dc.creator.none.fl_str_mv Puertas Centeno, David
Portesi, Mariela Adelina
author Puertas Centeno, David
author_facet Puertas Centeno, David
Portesi, Mariela Adelina
author_role author
author2 Portesi, Mariela Adelina
author2_role author
dc.subject.none.fl_str_mv UNCERTAINTY RELATIONS
INFORMATION ENTROPY
QUANTUM GRAVITY
topic UNCERTAINTY RELATIONS
INFORMATION ENTROPY
QUANTUM GRAVITY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The well-known Heisenberg-Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system. Different modified commutation relations have been considered in the last years with the purpose of taking into account the effect of quantum gravity. Indeed it can be seen that letting [X,P]=iℏ(1+β P^2) implies the existence of a minimal length proportional to sqrt(β). The Bialynicki-Birula-Mycielski entropic uncertainty relation in terms of Shannon entropies is also seen to be deformed in the presence of a minimal length, corresponding to a strictly positive deformation parameter β. Generalized entropies can be implemented. Indeed, results for the sum of position and (auxiliary) momentum Rényi entropies with conjugated indices have been provided recently for the ground and first excited state. We present numerical findings for conjugated pairs of entropic indices, for the lowest lying levels of the deformed harmonic oscillator system in 1D, taking into account the position distribution for the wavefunction and the actual momentum.
Fil: Puertas Centeno, David. Universidad Rey Juan Carlos; España
Fil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
description The well-known Heisenberg-Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system. Different modified commutation relations have been considered in the last years with the purpose of taking into account the effect of quantum gravity. Indeed it can be seen that letting [X,P]=iℏ(1+β P^2) implies the existence of a minimal length proportional to sqrt(β). The Bialynicki-Birula-Mycielski entropic uncertainty relation in terms of Shannon entropies is also seen to be deformed in the presence of a minimal length, corresponding to a strictly positive deformation parameter β. Generalized entropies can be implemented. Indeed, results for the sum of position and (auxiliary) momentum Rényi entropies with conjugated indices have been provided recently for the ground and first excited state. We present numerical findings for conjugated pairs of entropic indices, for the lowest lying levels of the deformed harmonic oscillator system in 1D, taking into account the position distribution for the wavefunction and the actual momentum.
publishDate 2019
dc.date.none.fl_str_mv 2019-11-19
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/128839
Puertas Centeno, David; Portesi, Mariela Adelina; Entropic Analysis of the Quantum Oscillator with a Minimal Length; Multidisciplinary Digital Publishing Institute; Proceedings; 12; 1; 19-11-2019; 1-4
2504-3900
CONICET Digital
CONICET
url http://hdl.handle.net/11336/128839
identifier_str_mv Puertas Centeno, David; Portesi, Mariela Adelina; Entropic Analysis of the Quantum Oscillator with a Minimal Length; Multidisciplinary Digital Publishing Institute; Proceedings; 12; 1; 19-11-2019; 1-4
2504-3900
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/2504-3900/12/1/57
info:eu-repo/semantics/altIdentifier/doi/10.3390/proceedings2019012057
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842980921031000064
score 12.993085

Publicaciones similares