Interactions and dynamics of one-dimensional droplets, bubbles and kinks

TL;DR

This paper investigates the complex interactions and dynamics of droplets, bubbles, and kinks in a one-dimensional quantum fluid model, revealing stability conditions, interaction behaviors, and phenomena observable in experiments.

Contribution

It provides a detailed analysis of the existence, stability, and interactions of droplets, bubbles, and kinks in the extended Gross-Pitaevskii model with Lee-Huang-Yang correction, including new dynamical insights.

Findings

Droplets are stable within certain chemical potential ranges.

Bubbles are unstable and tend to expand and attract.

Droplet-kink interactions lead to absorption and shock wave emission.

Abstract

We explore the dynamics and interactions of multiple bright droplets and bubbles, as well as the interactions of kinks with droplets and with antikinks, in the extended one-dimensional Gross-Pitaevskii model including the Lee-Huang-Yang correction. Existence regions are identified for the one-dimensional droplets and bubbles in terms of their chemical potential, verifying the stability of the droplets and exposing the instability of the bubbles. The limiting case of the droplet family is a stable kink. The interactions between droplets demonstrate in-phase (out-of-phase) attraction (repulsion), with the so-called Manton's method explicating the observed dynamical response, and mixed behavior for intermediate values of the phase shift. Droplets bearing different chemical potentials experience mass-exchange phenomena. Individual bubbles exhibit core expansion and mutual attraction prior to their destabilization. Droplets interacting with kinks are absorbed by them, a process accompanied by the emission of dispersive shock waves and gray solitons. Kink-antikink interactions are repulsive, generating counter-propagating shock waves. Our findings reveal dynamical features of droplets and kinks that can be detected in current experiments.