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arXiv:2207.13360 · Communications in Theoretical Physics

High precision solutions to quantized vortices within Gross–Pitaevskii equation

Hao-Hao Peng, Jian Deng, Sen‐Yue Lou, Qun Wang

Published Aug 4, 2022• 0 citations
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Abstract

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 very high precision is proposed. Through two-point Padé 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 Padé approximants are discussed. This investigation may shed light on the exact solution to the nonlinear vortex equation.

DOI
10.1088/1572-9494/ac86bd

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Pade approximants are used to find approximate vortex solutions of any winding number in the context of Gross-Pitaevskii equation for a uniform condensate and condensates with axisymmetric trapping potentials. Rational function and generalised rational function approximations of axisymmetric solitary waves of the Gross-Pitaevskii equation are obtained in two and three dimensions. These approximations are used to establish a new mechanism of vortex nucleation as a result of solitary wave interactions.
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Padé approximants are used to find the approximate vortex solutions of any winding number in the context of Gross-Pitaevskii equation for the uniform condensate and condensates with axisymmetric trapping potentials. The approximate solutions are used to elucidate the annihilation of pair of vortices of opposite circulation by finding the approximation to the streamfunction of the flow generated by such a pair. The critical velocity and minimal separation of vortices are calculated. Keywords: Gross-Pitaevskii model, Padé approximations, vortex solutions. 1