Statics and dynamics of a self-bound matter-wave quantum ball

TL;DR

This paper investigates the stability, collisions, and reflection behavior of a three-dimensional self-bound matter-wave quantum ball, demonstrating its soliton-like properties and the formation of a larger breather upon low-velocity collision.

Contribution

It provides a combined analytical and numerical analysis of the statics and dynamics of a stable, mobile quantum ball in three dimensions, highlighting its soliton-like collision and reflection properties.

Findings

Quantum balls are stable and can propagate in free space.

High-velocity collisions are quasi-elastic with no shape change.

Low-velocity collisions lead to coalescence forming a quantum-ball breather.

Abstract

We study the statics and dynamics of a stable, mobile, three-dimensional matter-wave spherical quantum ball created in the presence of an attractive two-body and a very small repulsive three-body interaction. The quantum ball can propagate with a constant velocity in any direction in free space and its stability under a small perturbation is established numerically and variationally. In frontal head-on and angular collisions at large velocities two quantum balls behave like quantum solitons. Such collision is found to be quasi elastic and the quantum balls emerge after collision without any change of direction of motion and velocity and with practically no deformation in shape. When reflected by a hard impenetrable plane, the quantum ball bounces off like a wave obeying the law of reflection without any change of shape or speed. However, in a collision at small velocities two quantum balls coalesce to form a larger ball which we call a quantum-ball breather. We point out the similarity and difference between the collision of two quantum and classical balls. The present study is based on an analytic variational approximation and a full numerical solution of the mean-field Gross-Pitaevskii equation using the parameters of $^7$Li atoms.