# Interaction of One-Dimensional Quantum Droplets with Potential Wells and Barriers

## TL;DR

This paper investigates the static and dynamic behaviors of one-dimensional quantum droplets interacting with potential wells and barriers, revealing stable localized states, collision outcomes, and counter-intuitive rebound phenomena through analytical and numerical methods.

## Contribution

It introduces exact solutions for localized states in 1D quantum droplets interacting with delta-function potentials and analyzes their collision dynamics using approximations and simulations.

## Key findings

- Stable localized states pinned to the well are found.
- Quantum droplets can rebound from potential wells, contrary to intuition.
- Collision outcomes include fission into transmitted, reflected, and trapped fragments.

## Abstract

We address static and dynamical properties of one-dimensional (1D) quantum droplets (QDs) under the action of local potentials in the form of narrow wells and barriers. The QDs are governed by the 1D Gross-Pitaevskii equation including the mean-field cubic repulsive term and the beyond-mean-field attractive quadratic one. In the case of the well represented by the delta-functional potential, three exact stable solutions are found for localized states pinned to the well. The Thomas-Fermi approximation for the well and the adiabatic approximation for the collision of the QD with the barrier are developed too. Collisions of incident QDs with the wells and barriers are analyzed in detail by means of systematic simulations. Outcomes, such as fission of the moving QD into transmitted, reflected, and trapped fragments, are identified in relevant parameter planes. In particular, a counter-intuitive effect of partial or full rebound of the incident QD from the potential well is studied in detail and qualitatively explained.