Energy-dependent scattering and the Gross-Pitaevskii equation in two-dimensional Bose-Einstein condensates

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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DYNAMICS OF VORTICES IN TWO-DIMENSIONAL BOSE–EINSTEIN CONDENSATES

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127402004644 ◽

2002 ◽

Vol 12 (04) ◽

pp. 739-764 ◽

Cited By ~ 5

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.

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Dipolar condensed atomic mixtures and miscibility under rotation

SciPost Physics Proceedings ◽

10.21468/scipostphysproc.3.023 ◽

2020 ◽

Author(s):

Lauro Tomio ◽

Ramavarmaraja Kishor Kumar ◽

Arnaldo Gammal

Keyword(s):

Binary Mixtures ◽

Spatial Separation ◽

Pitaevskii Equation ◽

Polarization Angle ◽

Two Dimensional ◽

Dipole Interactions ◽

Quartic Term ◽

Vortex Patterns ◽

Bose Einstein ◽

Dipole Polarization

By considering symmetric- and asymmetric-dipolar coupled mixtures (with dysprosium and erbium isotopes), we report a study on relevant anisotropic effects, related to spatial separation and miscibility, due to dipole-dipole interactions (DDIs) in rotating binary dipolar Bose-Einstein condensates. The binary mixtures are kept in strong pancake-like traps, with repulsive two-body interactions modeled by an effective two-dimensional (2D) coupled Gross-Pitaevskii equation. The DDI are tuned from repulsive to attractive by varying the dipole polarization angle. A clear spatial separation is verified in the densities for attractive DDIs, being angular for symmetric mixtures and radial for asymmetric ones. Also relevant is the mass-imbalance sensibility observed by the vortex-patterns in symmetric- and asymmetric-dipolar mixtures. In an extension of this study, here we show how the rotational properties and spatial separation of these dipolar mixture are affected by a quartic term added to the harmonic trap of one of the components.

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