TY - JOUR

T1 - Dynamics of vortex dipoles in anisotropic bose-Einstein condensates

AU - Goodman, Roy H.

AU - Kevrekidis, P. G.

AU - Carretero-González, R.

N1 - Publisher Copyright:
© 2015 Society for Industrial and Applied Mathematics.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2015

Y1 - 2015

N2 - We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ODEs describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. We uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals in the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system, we are able to construct complex periodic orbits in the original, PDE, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations.

AB - We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ODEs describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. We uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals in the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system, we are able to construct complex periodic orbits in the original, PDE, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations.

KW - Bose-Einstein condensates

KW - Gross-Pitaevskii equation

KW - Hamiltonian ODEs

KW - Nonlinear Schrodinger equation

KW - Vortex dynamics

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U2 - 10.1137/140992345

DO - 10.1137/140992345

M3 - Article

AN - SCOPUS:84937912486

VL - 14

SP - 699

EP - 729

JO - SIAM Journal on Applied Dynamical Systems

JF - SIAM Journal on Applied Dynamical Systems

SN - 1536-0040

IS - 2

ER -