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

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.
 [1] ;  [2] ;  [3]
  1. New Jersey Inst. of Technology, Newark, NJ (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. San Diego State Univ., San Diego, CA (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 1536-0040; TRN: US1600426
Grant/Contract Number:
Accepted Manuscript
Journal Name:
SIAM Journal on Applied Dynamical Systems
Additional Journal Information:
Journal Volume: 14; Journal Issue: 2; Journal ID: ISSN 1536-0040
Society for Industrial and Applied Mathematics
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
Country of Publication:
United States
74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICS AND COMPUTING; Vortex dynamics; nonlinear Schrodinger equation; Gross-Pitaevskii equation; Bose-Einstein condensates; Hamiltonian ODEs