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...

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Detalles Bibliográficos
Autores: Zamora, Darío Javier, Rocca, Mario Carlos, Plastino, Ángel Luis, Ferri, Gustavo Luis
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/63980
Acceso en línea:http://hdl.handle.net/11336/63980
Access Level:acceso abierto
Palabra clave:FIRST ORDER SOLUTION
NON-LINEAR KLEIN-GORDON EQUATION
NON-LINEAR SCHRÖDINGER EQUATION
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
Descripción
Sumario: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.