Barrier transmission for the Nonlinear Schr\"odinger Equation: Surprises of nonlinear transport

TL;DR

The paper reveals a surprising property of barrier transmission in nonlinear Schrödinger systems, where the potential can be split at any point into two parts with identical transmission, relevant for coherent transport studies.

Contribution

It uncovers an exact property of nonlinear wave functions related to barrier transmission, extending linear system insights to nonlinear regimes.

Findings

Barrier transmission in nonlinear Schrödinger systems exhibits a unique symmetry.

Potential can be divided at any point with identical transmission properties.

This property is relevant for Bose-Einstein condensate transport studies.

Abstract

In this communication we report on a peculiar property of barrier transmission that systems governed by the nonlinear Schroedinger equation share with the linear one: For unit transmission the potential can be divided at an arbitrary point into two sub-potentials, a left and a right one, which have exactly the same transmission. This is a rare case of an exact property of a nonlinear wave function which will be of interest, e.g., for studies of coherent transport of Bose-Einstein condensates through mesoscopic waveguide