Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

Goodman, Roy H.; Kevrekidis, P. G.; Carretero-González, R.

doi:10.1137/140992345

Title: Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

Journal Article · Tue Apr 14 00:00:00 EDT 2015 · SIAM Journal on Applied Dynamical Systems

DOI:https://doi.org/10.1137/140992345· OSTI ID:1233170

Goodman, Roy H. ^[1]; Kevrekidis, P. G. ^[2]; Carretero-González, R. ^[3]

New Jersey Inst. of Technology, Newark, NJ (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
San Diego State Univ., San Diego, CA (United States)

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. In this study, 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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1233170

Report Number(s):: LA-UR-14-28136; TRN: US1600426

Journal Information:: SIAM Journal on Applied Dynamical Systems, Vol. 14, Issue 2; ISSN 1536-0040

Publisher:: Society for Industrial and Applied MathematicsCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 9 works

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Title: Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

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