High precision solutions to quantized vortices within Gross-Pitaevskii equation

TL;DR

This paper introduces a highly precise method using two-point Padé approximants to solve the nonlinear vortex equations in the Gross-Pitaevskii framework, enhancing vortex simulation accuracy.

Contribution

The paper presents a systematic approach employing rational functions to achieve high-precision solutions for vortex equations in Bose-Einstein condensates.

Findings

Solutions are highly sensitive to parameters and truncation orders.

Precision improves with higher-order rational functions.

Discussion on errors and limitations of the method.

Abstract

The dynamics of vortices in Bose-Einstein condensates of dilute cold atoms can be well formulated by Gross-Pitaevskii equation. To better understand the properties of vortices, a systematic method to solve the nonlinear differential equation for the vortex to a very high precision is proposed. Through two-point Pad$\acute{\text{e}}$ approximants, these solutions are presented in terms of simple rational functions, which can be used in the simulation of vortex dynamics. The precision of the solutions is sensitive to the connecting parameter and the truncation orders. It can be improved significantly with a reasonable extension in the order of rational functions. The errors of the solutions and the limitation of two-point Pad$\acute{\text{e}}$ approximants are discussed. This investigation may shed light on the exact solution to the nonlinear vortex equation.