Kink-like Solitons in Quantum Droplet

TL;DR

This paper derives kink-like solitonic excitations in one-dimensional quantum droplets, revealing their structure, properties, and connections to classical compactons, with implications for understanding quantum fluid dynamics.

Contribution

It introduces a new class of kink-like solitons in quantum droplets, linking them to classical compactons and elliptic functions, expanding the understanding of quantum fluid excitations.

Findings

Identified kink-like solitons connecting vacuum and flat-top droplets

Determined soliton properties based on mean-field and quantum corrections

Connected solutions to elliptic functions via M"obius transform

Abstract

Solitonic excitations of the one-dimensional quantum droplets are obtained, which smoothly connect vacuum with the flat-top droplet, akin to compactons in classical liquids. These solitons are of the kink type, necessarily residing on a constant pedestal, determined by the mean-field repulsion and beyond mean field quantum correction and having exactly one-third of the uniform condensate amplitude. Akin to the kinks, the propagating modes occur in pairs and are phase-locked with the background. The lowest chemical potential and condensate amplitude at the flat-top boundary matches with the self-trapped quantum droplet. More general excitations of analogous kind are obtained through the M\"obius transform, which connect the required solutions to elliptic functions in general.