Localization phenomena in Nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose-Einstein condensates

TL;DR

This paper investigates how ground states of nonlinear Schrödinger equations with spatially varying interactions localize in regions where interactions vanish, with implications for Bose-Einstein condensates.

Contribution

It provides a theoretical analysis of localization phenomena in inhomogeneous nonlinear Schrödinger equations and discusses their relevance to Bose-Einstein condensates.

Findings

Ground states localize where interactions vanish.

Tunneling to regions with positive interactions is suppressed.

Chemical potential has a finite cutoff value.

Abstract

We study the properties of the ground state of Nonlinear Schr\"odinger Equations with spatially inhomogeneous interactions and show that it experiences a strong localization on the spatial region where the interactions vanish. At the same time, tunneling to regions with positive values of the interactions is strongly supressed by the nonlinear interactions and as the number of particles is increased it saturates in the region of finite interaction values. The chemical potential has a cutoff value in these systems and thus takes values on a finite interval. The applicability of the phenomenon to Bose-Einstein condensates is discussed in detail.