Properties of some nonlinear Schrödinger equations motivated through information theory

Abstract

We update our understanding of nonlinear Schrödinger 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 t] - 1/4 for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, t] might be encoding relativistic effects. © 2009 IOP Publishing Ltd.