DYNAMICS OF VORTICES IN TWO-DIMENSIONAL BOSE–EINSTEIN CONDENSATES

2002 ◽  
Vol 12 (04) ◽  
pp. 739-764 ◽  
Author(s):  
SHU-MING CHANG ◽  
WEN-WEI LIN ◽  
TAI-CHIA LIN
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Time Dependent ◽  
Pitaevskii Equation ◽  
Two Dimensional ◽  
Motion Equations ◽  
Trap Potential ◽  
Asymptotic Motion ◽  
Bose Einstein ◽  
Kirchhoff Problem

We derive the asymptotic motion equations of vortices for the time-dependent Gross–Pitaevskii equation with a harmonic trap potential. The asymptotic motion equations form a system of ordinary differential equations which can be regarded as a perturbation of the standard Kirchhoff problem. From the numerical simulation on the asymptotic motion equations, we observe that the bounded and collisionless trajectories of three vortices form chaotic, quasi 2- or quasi 3-periodic orbits. Furthermore, a new phenomenon of 1:1-topological synchronization is observed in the chaotic trajectories of two vortices.

scholarly journals A tale of two distributions: from few to many vortices in quasi-two-dimensional Bose–Einstein condensates

2014 ◽  
Vol 470 (2168) ◽  
pp. 20140048 ◽  
Author(s):  
T. Kolokolnikov ◽  
P. G. Kevrekidis ◽  
R. Carretero-González
Keyword(s):  
Differential Equations ◽  
Symmetry Breaking ◽  
Ordinary Differential Equations ◽  
Classical Result ◽  
Coarse Graining ◽  
Two Dimensional ◽  
Continuum Approach ◽  
Accurate Identification ◽  
Central Vortex ◽  
Bose Einstein

Motivated by the recent successes of particle models in capturing the precession and interactions of vortex structures in quasi-two-dimensional Bose–Einstein condensates, we revisit the relevant systems of ordinary differential equations. We consider the number of vortices N as a parameter and explore the prototypical configurations (‘ground states’) that arise in the case of few or many vortices. In the case of few vortices, we modify the classical result illustrating that vortex polygons in the form of a ring are unstable for N ≥7. Additionally, we reconcile this modification with the recent identification of symmetry-breaking bifurcations for the cases of N =2,…,5. We also briefly discuss the case of a ring of vortices surrounding a central vortex (so-called N +1 configuration). We finally examine the opposite limit of large N and illustrate how a coarse-graining, continuum approach enables the accurate identification of the radial distribution of vortices in that limit.

Exact solutions of the Gross-Pitaevskii equation for stable vortex modes in two-dimensional Bose-Einstein condensates

2010 ◽  
Vol 81 (6) ◽  
Author(s):  
Lei Wu ◽  
Lu Li ◽  
Jie-Fang Zhang ◽  
Dumitru Mihalache ◽  
Boris A. Malomed ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Pitaevskii Equation ◽  
Two Dimensional ◽  
Bose Einstein ◽  
Stable Vortex

scholarly journals A method to create disordered vortex arrays in atomic Bose–Einstein condensates

2009 ◽  
Vol 87 (9) ◽  
pp. 1013-1019 ◽  
Author(s):  
Enikö J.M. Madarassy
Keyword(s):  
Wave Function ◽  
Quantum Turbulence ◽  
Einstein Condensate ◽  
Complex Conjugate ◽  
Pitaevskii Equation ◽  
Two Dimensional ◽  
Bose Einstein Condensate ◽  
Phase Profile ◽  
Bose Einstein

We suggest a method to create quantum turbulence (QT) in a trapped atomic Bose–Einstein condensate (BEC). By replacing in the upper half of our box the wave function, Ψ, with its complex conjugate, Ψ*, new negative vortices are introduced into the system. The simulations are performed by solving the two-dimensional Gross–Pitaevskii equation (2D GPE). We study the successive dynamics of the wave function by monitoring the evolution of density and phase profile.

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