A Topological Soliton Model for Ball Lightning: Theory and Numerical Verification with the 3D Gross-Pitaevskii Equation

TL;DR

This paper introduces a topological soliton model for ball lightning, supported by numerical simulations of the 3D Gross-Pitaevskii equation, explaining its stability, longevity, and observational features.

Contribution

It proposes a novel topological soliton framework for ball lightning, verified through numerical simulations, linking atmospheric phenomena to Bose-Einstein condensate physics.

Findings

Solitons with topological charge are long-lived and stable.

Low transmission probability due to orthogonality with ground state.

Energy and size scales match observed ball lightning properties.

Abstract

Ball lightning is one of the most mysterious atmospheric phenomena, whose long lifetime, penetrative ability, and stability are difficult to explain with traditional physical models. This paper proposes a novel theoretical framework, interpreting ball lightning as a projection of a high-dimensional topological soliton into three-dimensional space. Its essence is described by a nonlinear Schr\"odinger equation with attractive interaction, protected by a non-zero topological charge. Through numerical simulation of the three-dimensional Gross-Pitaevskii equation, we verify the core predictions of this model: in a Bose-Einstein condensate with attractive interactions, solitons carrying topological charge exhibit: (1)long-lived stability (topological charge conserved under perturbations); (2)low transmission probability (due to minimal overlap integral resulting from orthogonality with the ground state wavefunction); (3)energy and size scales consistent with actual observations. Theoretical analysis indicates that the soliton lifetime is governed by the system's decoherence rate, providing a natural explanation for the observed second-scale lifetimes. This work not only offers a self-consistent physical explanation for ball lightning but also provides a concrete scheme for the experimental preparation and observation of three-dimensional topological solitons.