Bright Matter-Wave Soliton Collisions in a Harmonic Trap: Regular and Chaotic Dynamics

TL;DR

This paper investigates the dynamics of bright matter-wave soliton collisions in a harmonic trap, revealing both regular and chaotic behaviors through a particle analogy and wave simulations, advancing understanding of chaos in wave systems.

Contribution

It introduces a particle model for soliton collisions in a harmonic trap and demonstrates its effectiveness in capturing both regular and chaotic dynamics in Bose-Einstein condensates.

Findings

Particle model accurately predicts soliton collision outcomes

Chaotic regimes emerge in three-particle extensions

Good agreement between model and wave simulations

Abstract

Collisions between bright solitary waves in the 1D Gross-Pitaevskii equation with a harmonic potential, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. A particle analogy for the solitary waves is formulated, which is shown to be integrable for a two-particle system. The extension to three particles is shown to support chaotic regimes. Good agreement is found between the particle model and simulations of the full wave dynamics, suggesting that the dynamics can be described in terms of solitons both in regular and chaotic regimes, thus presenting a paradigm for chaos in wave-mechanics.