Properties of some nonlinear Schrodinger equations motivated through information theory

TL;DR

This paper explores properties of nonlinear Schrödinger equations derived from information theory, revealing how q-deformations affect energy and linking energy minimization to uncertainty maximization, with implications for supersymmetry and relativistic effects.

Contribution

It demonstrates that q-deformations increase system energy and connects energy minimization to uncertainty maximization, highlighting the significance of the parameter η in supersymmetry preservation.

Findings

q-deformation increases system energy

Energy minimization aligns with uncertainty maximization

Special η value preserves supersymmetry

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 $\eta =1/4$ for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, $\eta$ might be encoding relativistic effects.