Properties of some nonlinear Schrodinger equations motivated through information theory

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We update our understanding of nonlinear Schrodinger equations motivated through information theory. In particular we show that a $q-$deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouring the simplest $q=1$ case. Furthermore the energy minimisation criterion is shown to be equivalent, at leading order, to an uncertainty maximisation argument. The special value $η=1/4$ for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, $η$ might be encoding relativistic effects.
5 pages. Presented at the DICE 2008 workshop in Italy

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Quantum Physics, Pattern Formation and Solitons

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http://salesiana.dossiersoluciones.com/handle/123456789/220430

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0902.3044
 http://arxiv.org/abs/0902.3044

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arXiv