Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations

Interesting non-linear generalization of both Schrödinger’s and Klein–Gordon’s equations have been recently advanced by Tsallis, Rego-Monteiro and Tsallis (NRT) in Nobre et al. (Phys. Rev. Lett. 2011, 106, 140601). There is much current activity going on in this area. The non-linearity is governed b...

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Autores principales: Zamora, Darío Javier, Rocca, Mario Carlos, Plastino, Ángel Luis, Ferri, Gustavo L.
Formato: Articulo
Lenguaje:Inglés
Publicado: 2017
Materias:
Física
non-linear Schrödinger equation
non-linear Klein–Gordon equation
first order solution
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/78141
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-78141
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
non-linear Schrödinger equation
non-linear Klein–Gordon equation
first order solution
spellingShingle Física
non-linear Schrödinger equation
non-linear Klein–Gordon equation
first order solution
Zamora, Darío Javier
Rocca, Mario Carlos
Plastino, Ángel Luis
Ferri, Gustavo L.
Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations
topic_facet Física
non-linear Schrödinger equation
non-linear Klein–Gordon equation
first order solution
description Interesting non-linear generalization of both Schrödinger’s and Klein–Gordon’s equations have been recently advanced by Tsallis, Rego-Monteiro and Tsallis (NRT) in Nobre et al. (Phys. Rev. Lett. 2011, 106, 140601). There is much current activity going on in this area. The non-linearity is governed by a real parameter q. Empiric hints suggest that the ensuing non-linear q-Schrödinger and q-Klein–Gordon equations are a natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for q-values close to unity (Plastino et al. (Nucl. Phys. A 2016, 955, 16–26, Nucl. Phys. A 2016, 948, 19–27)). It might thus be difficult for q-values close to unity to ascertain whether one is dealing with solutions to the ordinary Schrödinger equation (whose free particle solutions are exponentials and for which q = 1) or with its NRT non-linear q -generalizations, whose free particle solutions are q-exponentials. In this work, we provide a careful analysis of the q ∼ 1 instance via a perturbative analysis of the NRT equations.
format Articulo
Articulo
author Zamora, Darío Javier
Rocca, Mario Carlos
Plastino, Ángel Luis
Ferri, Gustavo L.
author_facet Zamora, Darío Javier
Rocca, Mario Carlos
Plastino, Ángel Luis
Ferri, Gustavo L.
author_sort Zamora, Darío Javier
title Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations
title_short Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations
title_full Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations
title_fullStr Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations
title_full_unstemmed Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations
title_sort perturbative treatment of the non-linear q-schrödinger and q-klein–gordon equations
publishDate 2017
url http://sedici.unlp.edu.ar/handle/10915/78141
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AT roccamariocarlos perturbativetreatmentofthenonlinearqschrodingerandqkleingordonequations
AT plastinoangelluis perturbativetreatmentofthenonlinearqschrodingerandqkleingordonequations
AT ferrigustavol perturbativetreatmentofthenonlinearqschrodingerandqkleingordonequations
bdutipo_str Repositorios
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