Properties of some nonlinear Schrodinger equations motivated through information theory
Abstract
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.
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