The large nonlinearity scale limit of an information-theoretically motivated nonlinear Schrodinger equation

TL;DR

This paper investigates a nonlinear Schrödinger equation derived from the maximum uncertainty principle, focusing on the regime where the nonlinearity scale is large, revealing universal properties and stationary solutions.

Contribution

It analyzes the large nonlinearity scale limit of an information-theoretically motivated nonlinear Schrödinger equation, highlighting universality and stationary solutions.

Findings

Equation exhibits universality in the large nonlinearity scale regime

Stationary solutions are identified for a discretized version of the equation

The equation's properties are consistent with perturbative regime behaviors

Abstract

A nonlinear Schrodinger equation, that had been obtained within the context of the maximum uncertainty principle, has the form of a difference-differential equation and exhibits some interesting properties. Here we discuss that equation in the regime where the nonlinearity length scale is large compared to the deBroglie wavelength; just as in the perturbative regime, the equation again displays some universality. We also briefly discuss stationary solutions to a naturally induced discretisation of that equation.