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

• Autores: Zamora, Darío Javier; Rocca, Mario Carlos; Plastino, Ángel Luis; Ferri, Gustavo L.
• Año de publicación: 2017
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Física; non-linear Schrödinger equation; non-linear Klein–Gordon equation; first order solution
• Institución: Universidad Nacional de La Plata

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.
Facultad de Ciencias Exactas