Exact quantum revivals for the Dirac equation

Autores
Santillán, Osvaldo Pablo; Chamizo, Fernando
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the present work, the results obtained by Strange [Phys. Rev. Lett. 104, 120403 (2010)] about the revivals of a relativistic fermion wave function on a torus are considerably expanded. In fact, all the possible quantum states exhibiting revivals are fully characterized. The revivals are exact, that is, are true revivals without taking any particular limit such as the nonrelativistic one. The present results are of interest since they generalize the Talbot effect and the revivals of the Schrödinger equation to a relativistic situation with nonzero mass. This makes the problem nontrivial, as the dispersion relation is modified and is not linear. The present results are obtained by the use of arithmetic tools, which are described in certain detail. In addition, several plots of the revivals are presented, which are useful for exemplifying the procedure proposed in the present paper.
Fil: Santillán, Osvaldo Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Chamizo, Fernando. Universidad Autónoma de Madrid; España
Materia
REVIVALS
FRACTALS
DIRAC
NUMBRT
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:11336/234890
Acceder
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spelling Exact quantum revivals for the Dirac equationSantillán, Osvaldo PabloChamizo, FernandoREVIVALSFRACTALSDIRACNUMBRThttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In the present work, the results obtained by Strange [Phys. Rev. Lett. 104, 120403 (2010)] about the revivals of a relativistic fermion wave function on a torus are considerably expanded. In fact, all the possible quantum states exhibiting revivals are fully characterized. The revivals are exact, that is, are true revivals without taking any particular limit such as the nonrelativistic one. The present results are of interest since they generalize the Talbot effect and the revivals of the Schrödinger equation to a relativistic situation with nonzero mass. This makes the problem nontrivial, as the dispersion relation is modified and is not linear. The present results are obtained by the use of arithmetic tools, which are described in certain detail. In addition, several plots of the revivals are presented, which are useful for exemplifying the procedure proposed in the present paper.Fil: Santillán, Osvaldo Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Chamizo, Fernando. Universidad Autónoma de Madrid; EspañaAmerican Physical Society2024-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/234890Santillán, Osvaldo Pablo; Chamizo, Fernando; Exact quantum revivals for the Dirac equation; American Physical Society; Physical Review A; 109; 2; 2-2024; 1-20, 0222312469-9934CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.109.022231info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.022231info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2309.12471info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:33:28Zoai:ri.conicet.gov.ar:11336/234890instacron: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:34982025-09-29 10:33:28.875CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Exact quantum revivals for the Dirac equation
title Exact quantum revivals for the Dirac equation
spellingShingle Exact quantum revivals for the Dirac equation
Santillán, Osvaldo Pablo
REVIVALS
FRACTALS
DIRAC
NUMBRT
title_short Exact quantum revivals for the Dirac equation
title_full Exact quantum revivals for the Dirac equation
title_fullStr Exact quantum revivals for the Dirac equation
title_full_unstemmed Exact quantum revivals for the Dirac equation
title_sort Exact quantum revivals for the Dirac equation
dc.creator.none.fl_str_mv Santillán, Osvaldo Pablo
Chamizo, Fernando
author Santillán, Osvaldo Pablo
author_facet Santillán, Osvaldo Pablo
Chamizo, Fernando
author_role author
author2 Chamizo, Fernando
author2_role author
dc.subject.none.fl_str_mv REVIVALS
FRACTALS
DIRAC
NUMBRT
topic REVIVALS
FRACTALS
DIRAC
NUMBRT
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In the present work, the results obtained by Strange [Phys. Rev. Lett. 104, 120403 (2010)] about the revivals of a relativistic fermion wave function on a torus are considerably expanded. In fact, all the possible quantum states exhibiting revivals are fully characterized. The revivals are exact, that is, are true revivals without taking any particular limit such as the nonrelativistic one. The present results are of interest since they generalize the Talbot effect and the revivals of the Schrödinger equation to a relativistic situation with nonzero mass. This makes the problem nontrivial, as the dispersion relation is modified and is not linear. The present results are obtained by the use of arithmetic tools, which are described in certain detail. In addition, several plots of the revivals are presented, which are useful for exemplifying the procedure proposed in the present paper.
Fil: Santillán, Osvaldo Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Chamizo, Fernando. Universidad Autónoma de Madrid; España
description In the present work, the results obtained by Strange [Phys. Rev. Lett. 104, 120403 (2010)] about the revivals of a relativistic fermion wave function on a torus are considerably expanded. In fact, all the possible quantum states exhibiting revivals are fully characterized. The revivals are exact, that is, are true revivals without taking any particular limit such as the nonrelativistic one. The present results are of interest since they generalize the Talbot effect and the revivals of the Schrödinger equation to a relativistic situation with nonzero mass. This makes the problem nontrivial, as the dispersion relation is modified and is not linear. The present results are obtained by the use of arithmetic tools, which are described in certain detail. In addition, several plots of the revivals are presented, which are useful for exemplifying the procedure proposed in the present paper.
publishDate 2024
dc.date.none.fl_str_mv 2024-02
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/11336/234890
Santillán, Osvaldo Pablo; Chamizo, Fernando; Exact quantum revivals for the Dirac equation; American Physical Society; Physical Review A; 109; 2; 2-2024; 1-20, 022231
2469-9934
CONICET Digital
CONICET
url http://hdl.handle.net/11336/234890
identifier_str_mv Santillán, Osvaldo Pablo; Chamizo, Fernando; Exact quantum revivals for the Dirac equation; American Physical Society; Physical Review A; 109; 2; 2-2024; 1-20, 022231
2469-9934
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.109.022231
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.022231
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2309.12471
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 American Physical Society
publisher.none.fl_str_mv American Physical Society
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
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score 13.070432

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