The Gross-Pitaevskii Soliton: Relating Weakly and Strongly Repulsive Bosonic condensates and the magnetic soliton

TL;DR

This paper demonstrates a fundamental connection between the dark soliton solutions of the Gross-Pitaevskii equation for weakly repulsive bosons and the magnetic solitons in strongly repulsive hard core boson systems, linking BEC density to magnetization.

Contribution

It establishes a novel mapping between BEC density solitons and magnetic solitons in ferromagnets, bridging two different physical systems and enhancing understanding of their soliton characteristics.

Findings

GPE dark soliton describes strongly repulsive bosons at half filling.

Mapping relates BEC density to in-plane magnetization squared.

Provides intuitive understanding of soliton properties across systems.

Abstract

We show that the dark soliton of the Gross-Pitaevskii equation (GPE) that describes the Bose-Einstein condensate (BEC) density of a system of weakly repulsive bosons, also describes that of a system of strongly repulsive hard core bosons at half filling. This connection establishes a relationship between the GPE soliton and the magnetic soliton of an easy-plane ferromagnet, where the BEC density relates to the square of the in-plane magnetization of the system. This mapping between well known solitons in two distinct physical systems provides an intuitive understanding of various characteristics of the solitons.