scholarly journals Synchronization and Stabilization of Chaotic Dynamics in a Quasi-1D Bose-Einstein Condensate

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
B. A. Idowu ◽  
U. E. Vincent
Keyword(s):  
Chaotic Dynamics ◽  
Chaotic Oscillation ◽  
Stable State ◽  
Control Design ◽  
Lyapunov Stability Theory ◽  
Einstein Condensate ◽  
Control Technique ◽  
Bose Einstein Condensate ◽  
The Stability ◽  
Bose Einstein

A nonlinear control is proposed for the exponential stabilization and synchronization of chaotic behaviour in a model of Bose-Einstein condensate (BEC). The active control technique is designed based on Lyapunov stability theory and Routh-Hurwitz criteria. The control design approach in both cases guarantees the stability of the controlled states. Whereas the synchronization of two identical BEC in their chaotic states can be realized using the scheme; a suitable controller is also capable of driving the otherwise chaotic oscillation to a stable state which could be expected in practice. The effectiveness of this technique is theoretically and numerically demonstrated.

Nonlinear localized eigenmodes for a Bose–Einstein condensate in a double-well potential

2015 ◽  
Vol 29 (25) ◽  
pp. 1550150
Author(s):  
Qiongtao Xie ◽  
Xiaoliang Liu ◽  
Shiguang Rong
Keyword(s):  
Einstein Condensate ◽  
Localized Modes ◽  
Exact Analytical Solutions ◽  
Bose Einstein Condensate ◽  
Specific Choice ◽  
Asymmetric Distributions ◽  
The Stability ◽  
Bose Einstein ◽  
Double Well Potential ◽  
Potential Parameters

In this paper, we investigate the nonlinear localized eigenmodes for a Bose–Einstein condensate in a double-well potential. For a specific choice of the potential parameters, certain exact analytical solutions for nonlinear localized eigenmodes are presented. By applying the linear stability analysis, the stability regions of these exact nonlinear localized eigenmodes are obtained numerically. It is shown that under certain conditions, the unstable nonlinear localized modes display the breathing behavior characterized by repeated appearance of symmetric and asymmetric distributions in the two potentials. This breathing behavior is shown to arise from the symmetry breaking for these nonlinear localized eigenmodes.

Chaos control of a Bose–Einstein condensate in a moving optical lattice

2016 ◽  
Vol 30 (19) ◽  
pp. 1650238 ◽  
Author(s):  
Zhiying Zhang ◽  
Xiuqin Feng ◽  
Zhihai Yao
Keyword(s):  
Optical Lattice ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Lyapunov Stability Theory ◽  
Einstein Condensate ◽  
Control Parameters ◽  
Periodic Force ◽  
Bose Einstein Condensate ◽  
Bose Einstein

Chaos control of a Bose–Einstein condensate (BEC) loaded into a moving optical lattice with attractive interaction is investigated on the basis of Lyapunov stability theory. Three methods are designed to control chaos in BEC. As a controller, a bias constant, periodic force, or wavelet function feedback is added to the BEC system. Numerical simulations reveal that chaotic behavior can be well controlled to achieve periodicity by regulating control parameters. Different periodic orbits are available for different control parameters only if the maximal Lyapunov exponent of the system is negative. The abundant effect of chaotic control is also demonstrated numerically. Chaos control can be realized effectively by using our proposed control strategies.

scholarly journals Stability analysis of three-dimensional breather solitons in a Bose–Einstein condensate

2005 ◽  
Vol 461 (2063) ◽  
pp. 3561-3574 ◽  
Author(s):  
M Matuszewski ◽  
E Infeld ◽  
G Rowlands ◽  
M Trippenbach
Keyword(s):  
Three Dimensional ◽  
Einstein Condensate ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Stability Properties ◽  
Bose Einstein Condensate ◽  
The Stability ◽  
Bose Einstein ◽  
Dimensional Soliton

We investigated the stability properties of breather soliton trains in a three-dimensional Bose–Einstein condensate (BEC) with Feshbach-resonance management of the scattering length. This is done so as to generate both attractive and repulsive interaction. The condensate is confined only by a one-dimensional optical lattice and we consider strong, moderate and weak confinement. By strong confinement we mean a situation in which a quasi two-dimensional soliton is created. Moderate confinement admits a fully three-dimensional soliton. Weak confinement allows individual solitons to interact. Stability properties are investigated by several theoretical methods such as a variational analysis, treatment of motion in effective potential wells, and collapse dynamics. Armed with all the information forthcoming from these methods, we then undertake a numerical calculation. Our theoretical predictions are fully confirmed, perhaps to a higher degree than expected. We compare regions of stability in parameter space obtained from a fully three-dimensional analysis with those from a quasi two-dimensional treatment, when the dynamics in one direction are frozen. We find that in the three-dimensional case the stability region splits into two parts. However, as we tighten the confinement, one of the islands of stability moves toward higher frequencies and the lower frequency region becomes more and more like that for the quasi two-dimensional case. We demonstrate these solutions in direct numerical simulations and, importantly, suggest a way of creating robust three-dimensional solitons in experiments in a BEC in a one-dimensional lattice.

On the Stability of a Quantum Dynamics of a Bose-Einstein Condensate Trapped in a One-Dimensional Toroidal Geometry

2008 ◽  
Vol 47 (9) ◽  
pp. 2393-2408 ◽  
Author(s):  
G. P. Berman ◽  
A. R. Bishop ◽  
D. A. R. Dalvit ◽  
G. V. Shlyapnikov ◽  
N. Tarkhanov ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Einstein Condensate ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
The Stability ◽  
Bose Einstein ◽  
Toroidal Geometry
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