Localised nonlinear modes in the PT-symmetric double-delta well Gross-Pitaevskii equation

TL;DR

This paper constructs exact localized solutions for the PT-symmetric Gross-Pitaevskii equation with a double-delta well potential, revealing new nonlinear modes in a non-Hermitian quantum system.

Contribution

It provides explicit solutions and an analytical approach for the nonlinear PT-symmetric double-delta potential in the Gross-Pitaevskii equation, advancing understanding of localized modes in such systems.

Findings

Exact localized solutions expressed via transcendental equations

Analytical treatment of the linear PT-symmetric double-delta potential

Insights into nonlinear modes in non-Hermitian quantum systems

Abstract

We construct exact localised solutions of the PT-symmetric Gross-Pitaevskii equation with an attractive cubic nonlinearity. The trapping potential has the form of two $\delta$-function wells, where one well loses particles while the other one is fed with atoms at an equal rate. The parameters of the constructed solutions are expressible in terms of the roots of a system of two transcendental algebraic equations. We also furnish a simple analytical treatment of the linear Schr\"odinger equation with the PT-symmetric double-$\delta$ potential.