Properties of some nonlinear Schrodinger equations motivated through information theory - Quantum Physics

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Abstract: We update our understanding of nonlinear Schrodinger equations motivatedthrough information theory. In particular we show that a $q-$deformation of thebasic nonlinear equation leads to a perturbative increase in the energy of asystem, thus favouring the simplest $q=1$ case. Furthermore the energyminimisation criterion is shown to be equivalent, at leading order, to anuncertainty maximisation argument. The special value $\eta =1-4$ for theinterpolation parameter, where leading order energy shifts vanish, implies thepreservation of existing supersymmetry in nonlinearised supersymmetric quantummechanics. Physically, $\eta$ might be encoding relativistic effects.

Autor: Ding-Yuan Liew, Rajesh R. Parwani

Fuente: https://arxiv.org/