Stationary and uniformly accelerated states in nonlinear quantum mechanics

Autores
Plastino, Ángel Ricardo; Souza, A. M. C.; Nobre, F. D.; Tsallis, C.
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider two kinds of solutions of a recently proposed field theory leading to a nonlinear Schrödinger equation exhibiting solitonlike solutions of the power-law form eqi(kx-wt), involving the q exponential function naturally arising within nonextensive thermostatistics [eqz≡[1+(1-q)z]1/(1-q), with e1z=ez]. These fundamental solutions behave like free particles, satisfying p=k, E=ω, and E=p2/2m (1≤q<2). Here we introduce two additional types of exact, analytical solutions of the aforementioned field theory. As a first step we extend the theory to situations involving a potential energy term, thus going beyond the previous treatment concerning solely the free-particle dynamics. Then we consider both bound, stationary states associated with a confining potential and also time-evolving states corresponding to a linear potential function. These types of solutions might be relevant for physical applications of the present nonlinear generalized Schrödinger equation. In particular, the stationary solution obtained shows an increase in the probability for finding the particle localized around a certain position of the well as one increases q in the interval 1≤q<2, which should be appropriate for physical systems where one finds a low-energy particle localized inside a confining potential.
Fil: Plastino, Ángel Ricardo. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Bioinvestigaciones (Sede Junín); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Souza, A. M. C.. Universidade Federal de Sergipe; Brasil. National Institute of Science and Technology for Complex Systems; Brasil
Fil: Nobre, F. D.. National Institute of Science and Technology for Complex Systems; Brasil. Centro Brasileiro de Pesquisas Físicas; Brasil
Fil: Tsallis, C.. Centro Brasileiro de Pesquisas Físicas; Brasil. Santa Fe Institute; Estados Unidos. National Institute of Science and Technology for Complex Systems; Brasil
Materia
Nonlinear Schroedinger Equation
Exact Solutions
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:11336/37333
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Stationary and uniformly accelerated states in nonlinear quantum mechanicsPlastino, Ángel RicardoSouza, A. M. C.Nobre, F. D.Tsallis, C.Nonlinear Schroedinger EquationExact Solutionshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We consider two kinds of solutions of a recently proposed field theory leading to a nonlinear Schrödinger equation exhibiting solitonlike solutions of the power-law form eqi(kx-wt), involving the q exponential function naturally arising within nonextensive thermostatistics [eqz≡[1+(1-q)z]1/(1-q), with e1z=ez]. These fundamental solutions behave like free particles, satisfying p=k, E=ω, and E=p2/2m (1≤q<2). Here we introduce two additional types of exact, analytical solutions of the aforementioned field theory. As a first step we extend the theory to situations involving a potential energy term, thus going beyond the previous treatment concerning solely the free-particle dynamics. Then we consider both bound, stationary states associated with a confining potential and also time-evolving states corresponding to a linear potential function. These types of solutions might be relevant for physical applications of the present nonlinear generalized Schrödinger equation. In particular, the stationary solution obtained shows an increase in the probability for finding the particle localized around a certain position of the well as one increases q in the interval 1≤q<2, which should be appropriate for physical systems where one finds a low-energy particle localized inside a confining potential.Fil: Plastino, Ángel Ricardo. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Bioinvestigaciones (Sede Junín); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Souza, A. M. C.. Universidade Federal de Sergipe; Brasil. National Institute of Science and Technology for Complex Systems; BrasilFil: Nobre, F. D.. National Institute of Science and Technology for Complex Systems; Brasil. Centro Brasileiro de Pesquisas Físicas; BrasilFil: Tsallis, C.. Centro Brasileiro de Pesquisas Físicas; Brasil. Santa Fe Institute; Estados Unidos. National Institute of Science and Technology for Complex Systems; BrasilAmerican Physical Society2014-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/37333Plastino, Ángel Ricardo; Souza, A. M. C.; Nobre, F. D.; Tsallis, C.; Stationary and uniformly accelerated states in nonlinear quantum mechanics; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 90; 6; 12-20141050-2947CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.90.062134info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.90.062134info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:36:23Zoai:ri.conicet.gov.ar:11336/37333instacron: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 09:36:23.505CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Stationary and uniformly accelerated states in nonlinear quantum mechanics
title Stationary and uniformly accelerated states in nonlinear quantum mechanics
spellingShingle Stationary and uniformly accelerated states in nonlinear quantum mechanics
Plastino, Ángel Ricardo
Nonlinear Schroedinger Equation
Exact Solutions
title_short Stationary and uniformly accelerated states in nonlinear quantum mechanics
title_full Stationary and uniformly accelerated states in nonlinear quantum mechanics
title_fullStr Stationary and uniformly accelerated states in nonlinear quantum mechanics
title_full_unstemmed Stationary and uniformly accelerated states in nonlinear quantum mechanics
title_sort Stationary and uniformly accelerated states in nonlinear quantum mechanics
dc.creator.none.fl_str_mv Plastino, Ángel Ricardo
Souza, A. M. C.
Nobre, F. D.
Tsallis, C.
author Plastino, Ángel Ricardo
author_facet Plastino, Ángel Ricardo
Souza, A. M. C.
Nobre, F. D.
Tsallis, C.
author_role author
author2 Souza, A. M. C.
Nobre, F. D.
Tsallis, C.
author2_role author
author
author
dc.subject.none.fl_str_mv Nonlinear Schroedinger Equation
Exact Solutions
topic Nonlinear Schroedinger Equation
Exact Solutions
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider two kinds of solutions of a recently proposed field theory leading to a nonlinear Schrödinger equation exhibiting solitonlike solutions of the power-law form eqi(kx-wt), involving the q exponential function naturally arising within nonextensive thermostatistics [eqz≡[1+(1-q)z]1/(1-q), with e1z=ez]. These fundamental solutions behave like free particles, satisfying p=k, E=ω, and E=p2/2m (1≤q<2). Here we introduce two additional types of exact, analytical solutions of the aforementioned field theory. As a first step we extend the theory to situations involving a potential energy term, thus going beyond the previous treatment concerning solely the free-particle dynamics. Then we consider both bound, stationary states associated with a confining potential and also time-evolving states corresponding to a linear potential function. These types of solutions might be relevant for physical applications of the present nonlinear generalized Schrödinger equation. In particular, the stationary solution obtained shows an increase in the probability for finding the particle localized around a certain position of the well as one increases q in the interval 1≤q<2, which should be appropriate for physical systems where one finds a low-energy particle localized inside a confining potential.
Fil: Plastino, Ángel Ricardo. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Bioinvestigaciones (Sede Junín); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Souza, A. M. C.. Universidade Federal de Sergipe; Brasil. National Institute of Science and Technology for Complex Systems; Brasil
Fil: Nobre, F. D.. National Institute of Science and Technology for Complex Systems; Brasil. Centro Brasileiro de Pesquisas Físicas; Brasil
Fil: Tsallis, C.. Centro Brasileiro de Pesquisas Físicas; Brasil. Santa Fe Institute; Estados Unidos. National Institute of Science and Technology for Complex Systems; Brasil
description We consider two kinds of solutions of a recently proposed field theory leading to a nonlinear Schrödinger equation exhibiting solitonlike solutions of the power-law form eqi(kx-wt), involving the q exponential function naturally arising within nonextensive thermostatistics [eqz≡[1+(1-q)z]1/(1-q), with e1z=ez]. These fundamental solutions behave like free particles, satisfying p=k, E=ω, and E=p2/2m (1≤q<2). Here we introduce two additional types of exact, analytical solutions of the aforementioned field theory. As a first step we extend the theory to situations involving a potential energy term, thus going beyond the previous treatment concerning solely the free-particle dynamics. Then we consider both bound, stationary states associated with a confining potential and also time-evolving states corresponding to a linear potential function. These types of solutions might be relevant for physical applications of the present nonlinear generalized Schrödinger equation. In particular, the stationary solution obtained shows an increase in the probability for finding the particle localized around a certain position of the well as one increases q in the interval 1≤q<2, which should be appropriate for physical systems where one finds a low-energy particle localized inside a confining potential.
publishDate 2014
dc.date.none.fl_str_mv 2014-12
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/11336/37333
Plastino, Ángel Ricardo; Souza, A. M. C.; Nobre, F. D.; Tsallis, C.; Stationary and uniformly accelerated states in nonlinear quantum mechanics; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 90; 6; 12-2014
1050-2947
CONICET Digital
CONICET
url http://hdl.handle.net/11336/37333
identifier_str_mv Plastino, Ángel Ricardo; Souza, A. M. C.; Nobre, F. D.; Tsallis, C.; Stationary and uniformly accelerated states in nonlinear quantum mechanics; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 90; 6; 12-2014
1050-2947
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.90.062134
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.90.062134
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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