Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation

Autores
Curilef, S.; Plastino, Ángel Ricardo; Plastino, Ángel Luis
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Tsallis maximum entropy distributions provide useful tools for the study of a wide range of scenarios in mathematics, physics, and other fields. Here we apply a Tsallis maximum entropy ansatz, the q-Gaussian, to obtain time dependent wave-packet solutions to a nonlinear Schrödinger equation recently advanced by Nobre, Rego-Monteiro and Tsallis (NRT) [F.D. Nobre, M.A. Rego-Monteiro, C. Tsallis, Phys. Rev. Lett. 106 (2011) 140601]. The NRT nonlinear equation admits plane wave-like solutions (q-plane waves) compatible with the celebrated de Broglie relations connecting wave number and frequency, respectively, with energy and momentum. The NRT equation, inspired in the q-generalized thermostatistical formalism, is characterized by a parameter q and in the limit q→1 reduces to the standard, linear Schrödinger equation. The q-Gaussian solutions to the NRT equation investigated here admit as a particular instance the previously known q-plane wave solutions. The present work thus extends the range of possible processes yielded by the NRT dynamics that admit an analytical, exact treatment. In the q→1 limit the q-Gaussian solutions correspond to the Gaussian wave packet solutions to the free particle linear Schrödinger equation. In the present work we also show that there are other families of nonlinear Schrödinger-like equations, besides the NRT one, exhibiting a dynamics compatible with the de Broglie relations. Remarkably, however, the existence of time dependent Gaussian-like wave packet solutions is a unique feature of the NRT equation not shared by the aforementioned, more general, families of nonlinear evolution equations.
Fil: Curilef, S.. Departamento de Física. Universidad Católica del Norte. Antofagasta; Chile
Fil: Plastino, Ángel Ricardo. Universidad Nacional de La Plata. Centro Regional de Estudios Genómicos; Argentina. Universidad de Granada; España. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Plastino, Ángel Luis. 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. Universidad de las Islas Baleares; España. Consejo Superior de Investigaciones Cientificas; España
Materia
Tsallis Entropy
Nonlinear Scrhoedinger Equation
Power Laws
Wave Packets
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:11336/22548
Acceder
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spelling Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equationCurilef, S.Plastino, Ángel RicardoPlastino, Ángel LuisTsallis EntropyNonlinear Scrhoedinger EquationPower LawsWave Packetshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Tsallis maximum entropy distributions provide useful tools for the study of a wide range of scenarios in mathematics, physics, and other fields. Here we apply a Tsallis maximum entropy ansatz, the q-Gaussian, to obtain time dependent wave-packet solutions to a nonlinear Schrödinger equation recently advanced by Nobre, Rego-Monteiro and Tsallis (NRT) [F.D. Nobre, M.A. Rego-Monteiro, C. Tsallis, Phys. Rev. Lett. 106 (2011) 140601]. The NRT nonlinear equation admits plane wave-like solutions (q-plane waves) compatible with the celebrated de Broglie relations connecting wave number and frequency, respectively, with energy and momentum. The NRT equation, inspired in the q-generalized thermostatistical formalism, is characterized by a parameter q and in the limit q→1 reduces to the standard, linear Schrödinger equation. The q-Gaussian solutions to the NRT equation investigated here admit as a particular instance the previously known q-plane wave solutions. The present work thus extends the range of possible processes yielded by the NRT dynamics that admit an analytical, exact treatment. In the q→1 limit the q-Gaussian solutions correspond to the Gaussian wave packet solutions to the free particle linear Schrödinger equation. In the present work we also show that there are other families of nonlinear Schrödinger-like equations, besides the NRT one, exhibiting a dynamics compatible with the de Broglie relations. Remarkably, however, the existence of time dependent Gaussian-like wave packet solutions is a unique feature of the NRT equation not shared by the aforementioned, more general, families of nonlinear evolution equations.Fil: Curilef, S.. Departamento de Física. Universidad Católica del Norte. Antofagasta; ChileFil: Plastino, Ángel Ricardo. Universidad Nacional de La Plata. Centro Regional de Estudios Genómicos; Argentina. Universidad de Granada; España. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Plastino, Ángel Luis. 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. Universidad de las Islas Baleares; España. Consejo Superior de Investigaciones Cientificas; EspañaElsevier2013-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/22548Curilef, S.; Plastino, Ángel Ricardo; Plastino, Ángel Luis; Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation; Elsevier; Physica A: Statistical Mechanics and its Applications; 392; 11; 2-2013; 2631-26420378-4371CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0378437113001362info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physa.2012.12.041info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-17T11:08:06Zoai:ri.conicet.gov.ar:11336/22548instacron: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:34982025-09-17 11:08:07.189CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation
title Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation
spellingShingle Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation
Curilef, S.
Tsallis Entropy
Nonlinear Scrhoedinger Equation
Power Laws
Wave Packets
title_short Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation
title_full Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation
title_fullStr Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation
title_full_unstemmed Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation
title_sort Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation
dc.creator.none.fl_str_mv Curilef, S.
Plastino, Ángel Ricardo
Plastino, Ángel Luis
author Curilef, S.
author_facet Curilef, S.
Plastino, Ángel Ricardo
Plastino, Ángel Luis
author_role author
author2 Plastino, Ángel Ricardo
Plastino, Ángel Luis
author2_role author
author
dc.subject.none.fl_str_mv Tsallis Entropy
Nonlinear Scrhoedinger Equation
Power Laws
Wave Packets
topic Tsallis Entropy
Nonlinear Scrhoedinger Equation
Power Laws
Wave Packets
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Tsallis maximum entropy distributions provide useful tools for the study of a wide range of scenarios in mathematics, physics, and other fields. Here we apply a Tsallis maximum entropy ansatz, the q-Gaussian, to obtain time dependent wave-packet solutions to a nonlinear Schrödinger equation recently advanced by Nobre, Rego-Monteiro and Tsallis (NRT) [F.D. Nobre, M.A. Rego-Monteiro, C. Tsallis, Phys. Rev. Lett. 106 (2011) 140601]. The NRT nonlinear equation admits plane wave-like solutions (q-plane waves) compatible with the celebrated de Broglie relations connecting wave number and frequency, respectively, with energy and momentum. The NRT equation, inspired in the q-generalized thermostatistical formalism, is characterized by a parameter q and in the limit q→1 reduces to the standard, linear Schrödinger equation. The q-Gaussian solutions to the NRT equation investigated here admit as a particular instance the previously known q-plane wave solutions. The present work thus extends the range of possible processes yielded by the NRT dynamics that admit an analytical, exact treatment. In the q→1 limit the q-Gaussian solutions correspond to the Gaussian wave packet solutions to the free particle linear Schrödinger equation. In the present work we also show that there are other families of nonlinear Schrödinger-like equations, besides the NRT one, exhibiting a dynamics compatible with the de Broglie relations. Remarkably, however, the existence of time dependent Gaussian-like wave packet solutions is a unique feature of the NRT equation not shared by the aforementioned, more general, families of nonlinear evolution equations.
Fil: Curilef, S.. Departamento de Física. Universidad Católica del Norte. Antofagasta; Chile
Fil: Plastino, Ángel Ricardo. Universidad Nacional de La Plata. Centro Regional de Estudios Genómicos; Argentina. Universidad de Granada; España. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Plastino, Ángel Luis. 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. Universidad de las Islas Baleares; España. Consejo Superior de Investigaciones Cientificas; España
description Tsallis maximum entropy distributions provide useful tools for the study of a wide range of scenarios in mathematics, physics, and other fields. Here we apply a Tsallis maximum entropy ansatz, the q-Gaussian, to obtain time dependent wave-packet solutions to a nonlinear Schrödinger equation recently advanced by Nobre, Rego-Monteiro and Tsallis (NRT) [F.D. Nobre, M.A. Rego-Monteiro, C. Tsallis, Phys. Rev. Lett. 106 (2011) 140601]. The NRT nonlinear equation admits plane wave-like solutions (q-plane waves) compatible with the celebrated de Broglie relations connecting wave number and frequency, respectively, with energy and momentum. The NRT equation, inspired in the q-generalized thermostatistical formalism, is characterized by a parameter q and in the limit q→1 reduces to the standard, linear Schrödinger equation. The q-Gaussian solutions to the NRT equation investigated here admit as a particular instance the previously known q-plane wave solutions. The present work thus extends the range of possible processes yielded by the NRT dynamics that admit an analytical, exact treatment. In the q→1 limit the q-Gaussian solutions correspond to the Gaussian wave packet solutions to the free particle linear Schrödinger equation. In the present work we also show that there are other families of nonlinear Schrödinger-like equations, besides the NRT one, exhibiting a dynamics compatible with the de Broglie relations. Remarkably, however, the existence of time dependent Gaussian-like wave packet solutions is a unique feature of the NRT equation not shared by the aforementioned, more general, families of nonlinear evolution equations.
publishDate 2013
dc.date.none.fl_str_mv 2013-02
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/11336/22548
Curilef, S.; Plastino, Ángel Ricardo; Plastino, Ángel Luis; Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation; Elsevier; Physica A: Statistical Mechanics and its Applications; 392; 11; 2-2013; 2631-2642
0378-4371
CONICET Digital
CONICET
url http://hdl.handle.net/11336/22548
identifier_str_mv Curilef, S.; Plastino, Ángel Ricardo; Plastino, Ángel Luis; Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation; Elsevier; Physica A: Statistical Mechanics and its Applications; 392; 11; 2-2013; 2631-2642
0378-4371
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0378437113001362
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physa.2012.12.041
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 Elsevier
publisher.none.fl_str_mv Elsevier
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 13.000565

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