Supersymmetric soliton solution in (1+1)-dimensional Ultracold Quantum Gases

TL;DR

This paper derives a supersymmetric (1+1)-dimensional model from ultracold quantum gases, identifies supercharges, and finds new static self-dual solutions governed by a Liouville-type equation.

Contribution

It introduces a supersymmetric framework for ultracold quantum gases and discovers novel static solutions with self-duality properties.

Findings

Supercharges are correctly identified and their algebra constructed.

New static self-dual solutions satisfying a Liouville equation are found.

The model provides insights into supersymmetry in low-dimensional quantum gases.

Abstract

We obtain by dimensional reduction a $(1+1)$ supersymmetric system introduced in the description of ultracold quantum gases. The correct supercharges are identified and their algebra is constructed. Finally novel static self-dual solutions emerge, satisfying a Liouville type differential equation.