Long term dynamics of the splitting of a doubly quantized vortex in a two-dimensional condensate

TL;DR

This paper investigates the long-term nonlinear dynamics of a doubly quantized vortex splitting in a 2D condensate, using the Gross-Pitaevskii equation and a three-level system model to explain the process.

Contribution

It provides an analytical solution for vortex splitting dynamics and clarifies the roles of linear instability and nonlinear effects in the process.

Findings

Splitting time scale is mainly set by linear instability

Nonlinear effects contribute logarithmically to the dynamics

Analytical description matches numerical simulations

Abstract

We study the nonlinear dynamics of the splitting of a doubly quantized vortex in a trapped condensate. The dynamics is studied in detail by solving the Gross-Pitaevskii equation. The main dynamical features are explained in terms of a nonlinear three-level system. We find an analytical solution for the characteristics of the dynamics. It is concluded that the time scale for the splitting is mainly determined by the instability of the linearized system, and nonlinear effects contribute logarithmically.