Nonlinear Schroedinger equation in the presence of uniform acceleration

Autores
Plastino, Ángel Ricardo; Tsallis, C.
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider a recently proposed nonlinear Schroedinger equation exhibiting solitonlike solutions of the power-law form ei(kx−wt) q , involving the q-exponential function which naturally emerges within nonextensive thermostatistics [ez q ≡ [1 + (1 − q)z] 1/(1−q) , with ez 1 = ez ]. Since these basic solutions behave like free particles, obeying p = k, E = ω, and E = p2/2m (1 ≤ q < 2), it is relevant to investigate how they change under the effect of uniform acceleration, thus providing the first steps towards the application of the aforementioned nonlinear equation to the study of physical scenarios beyond free particle dynamics. We investigate first the behaviour of the power-law solutions under Galilean transformation and discuss the ensuing Doppler-like effects. We consider then constant acceleration, obtaining new solutions that can be equivalently regarded as describing a free particle viewed from an uniformly accelerated reference frame (with acceleration a) or a particle moving under a constant force − ma. The latter interpretation naturally leads to the evolution equation i ∂ ∂t 0 = − 1 2−q 2 2m ∂2 ∂x2 0 2−q + V(x) 0 q with V(x) = max. Remarkably enough, the potential V couples to q, instead of coupling to , as happens in the familiar linear case (q = 1).
Fil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires; Argentina. Universidad de Granada; España
Fil: Tsallis, C.. Centro Brasileiro de Pesquisas F´ısicas and National Institute of Science and Technology for Complex Systems; Brasil. Santa Fe Institute; México
Materia
Nonlinear Schroedinger Equation
Uniform Acceleration
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:11336/24282
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/24282
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network_name_str CONICET Digital (CONICET)
spelling Nonlinear Schroedinger equation in the presence of uniform accelerationPlastino, Ángel RicardoTsallis, C.Nonlinear Schroedinger EquationUniform Accelerationhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We consider a recently proposed nonlinear Schroedinger equation exhibiting solitonlike solutions of the power-law form ei(kx−wt) q , involving the q-exponential function which naturally emerges within nonextensive thermostatistics [ez q ≡ [1 + (1 − q)z] 1/(1−q) , with ez 1 = ez ]. Since these basic solutions behave like free particles, obeying p = k, E = ω, and E = p2/2m (1 ≤ q < 2), it is relevant to investigate how they change under the effect of uniform acceleration, thus providing the first steps towards the application of the aforementioned nonlinear equation to the study of physical scenarios beyond free particle dynamics. We investigate first the behaviour of the power-law solutions under Galilean transformation and discuss the ensuing Doppler-like effects. We consider then constant acceleration, obtaining new solutions that can be equivalently regarded as describing a free particle viewed from an uniformly accelerated reference frame (with acceleration a) or a particle moving under a constant force − ma. The latter interpretation naturally leads to the evolution equation i ∂ ∂t 0 = − 1 2−q 2 2m ∂2 ∂x2 0 2−q + V(x) 0 q with V(x) = max. Remarkably enough, the potential V couples to q, instead of coupling to , as happens in the familiar linear case (q = 1).Fil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires; Argentina. Universidad de Granada; EspañaFil: Tsallis, C.. Centro Brasileiro de Pesquisas F´ısicas and National Institute of Science and Technology for Complex Systems; Brasil. Santa Fe Institute; MéxicoAmerican Institute of Physics2013-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/24282Plastino, Ángel Ricardo; Tsallis, C.; Nonlinear Schroedinger equation in the presence of uniform acceleration; American Institute of Physics; Journal of Mathematical Physics; 54; 4; 4-2013; 41505-415100022-2488CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1063/1.4798999info:eu-repo/semantics/altIdentifier/url/http://aip.scitation.org/doi/10.1063/1.4798999info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:50:54Zoai:ri.conicet.gov.ar:11336/24282instacron: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:34982025-09-03 09:50:55.662CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Nonlinear Schroedinger equation in the presence of uniform acceleration
title Nonlinear Schroedinger equation in the presence of uniform acceleration
spellingShingle Nonlinear Schroedinger equation in the presence of uniform acceleration
Plastino, Ángel Ricardo
Nonlinear Schroedinger Equation
Uniform Acceleration
title_short Nonlinear Schroedinger equation in the presence of uniform acceleration
title_full Nonlinear Schroedinger equation in the presence of uniform acceleration
title_fullStr Nonlinear Schroedinger equation in the presence of uniform acceleration
title_full_unstemmed Nonlinear Schroedinger equation in the presence of uniform acceleration
title_sort Nonlinear Schroedinger equation in the presence of uniform acceleration
dc.creator.none.fl_str_mv Plastino, Ángel Ricardo
Tsallis, C.
author Plastino, Ángel Ricardo
author_facet Plastino, Ángel Ricardo
Tsallis, C.
author_role author
author2 Tsallis, C.
author2_role author
dc.subject.none.fl_str_mv Nonlinear Schroedinger Equation
Uniform Acceleration
topic Nonlinear Schroedinger Equation
Uniform Acceleration
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 a recently proposed nonlinear Schroedinger equation exhibiting solitonlike solutions of the power-law form ei(kx−wt) q , involving the q-exponential function which naturally emerges within nonextensive thermostatistics [ez q ≡ [1 + (1 − q)z] 1/(1−q) , with ez 1 = ez ]. Since these basic solutions behave like free particles, obeying p = k, E = ω, and E = p2/2m (1 ≤ q < 2), it is relevant to investigate how they change under the effect of uniform acceleration, thus providing the first steps towards the application of the aforementioned nonlinear equation to the study of physical scenarios beyond free particle dynamics. We investigate first the behaviour of the power-law solutions under Galilean transformation and discuss the ensuing Doppler-like effects. We consider then constant acceleration, obtaining new solutions that can be equivalently regarded as describing a free particle viewed from an uniformly accelerated reference frame (with acceleration a) or a particle moving under a constant force − ma. The latter interpretation naturally leads to the evolution equation i ∂ ∂t 0 = − 1 2−q 2 2m ∂2 ∂x2 0 2−q + V(x) 0 q with V(x) = max. Remarkably enough, the potential V couples to q, instead of coupling to , as happens in the familiar linear case (q = 1).
Fil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires; Argentina. Universidad de Granada; España
Fil: Tsallis, C.. Centro Brasileiro de Pesquisas F´ısicas and National Institute of Science and Technology for Complex Systems; Brasil. Santa Fe Institute; México
description We consider a recently proposed nonlinear Schroedinger equation exhibiting solitonlike solutions of the power-law form ei(kx−wt) q , involving the q-exponential function which naturally emerges within nonextensive thermostatistics [ez q ≡ [1 + (1 − q)z] 1/(1−q) , with ez 1 = ez ]. Since these basic solutions behave like free particles, obeying p = k, E = ω, and E = p2/2m (1 ≤ q < 2), it is relevant to investigate how they change under the effect of uniform acceleration, thus providing the first steps towards the application of the aforementioned nonlinear equation to the study of physical scenarios beyond free particle dynamics. We investigate first the behaviour of the power-law solutions under Galilean transformation and discuss the ensuing Doppler-like effects. We consider then constant acceleration, obtaining new solutions that can be equivalently regarded as describing a free particle viewed from an uniformly accelerated reference frame (with acceleration a) or a particle moving under a constant force − ma. The latter interpretation naturally leads to the evolution equation i ∂ ∂t 0 = − 1 2−q 2 2m ∂2 ∂x2 0 2−q + V(x) 0 q with V(x) = max. Remarkably enough, the potential V couples to q, instead of coupling to , as happens in the familiar linear case (q = 1).
publishDate 2013
dc.date.none.fl_str_mv 2013-04
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/11336/24282
Plastino, Ángel Ricardo; Tsallis, C.; Nonlinear Schroedinger equation in the presence of uniform acceleration; American Institute of Physics; Journal of Mathematical Physics; 54; 4; 4-2013; 41505-41510
0022-2488
CONICET Digital
CONICET
url http://hdl.handle.net/11336/24282
identifier_str_mv Plastino, Ángel Ricardo; Tsallis, C.; Nonlinear Schroedinger equation in the presence of uniform acceleration; American Institute of Physics; Journal of Mathematical Physics; 54; 4; 4-2013; 41505-41510
0022-2488
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1063/1.4798999
info:eu-repo/semantics/altIdentifier/url/http://aip.scitation.org/doi/10.1063/1.4798999
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 Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
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 13.13397

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