Onto the stability analysis of hyperbolic secant-shaped Bose-Einstein condensate

2018 ◽  
Author(s):  
S. Sabari ◽  
R. Murali
Keyword(s):  
Stability Analysis ◽  
Einstein Condensate ◽  
Bose Einstein Condensate ◽  
The Stability ◽  
Bose Einstein

scholarly journals Stability analysis of a Bose–Einstein condensate trapped in a generic potential

2018 ◽  
Vol 72 (9) ◽  
Author(s):  
Elías Castellanos ◽  
Celia Escamilla-Rivera ◽  
Mayra J. Reyes-Ibarra
Keyword(s):  
Stability Analysis ◽  
Einstein Condensate ◽  
Bose Einstein Condensate ◽  
Bose Einstein

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.

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.

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

scholarly journals Scalar field as a Bose–Einstein condensate in a Schwarzschild–de Sitter spacetime

2017 ◽  
Vol 26 (04) ◽  
pp. 1750032 ◽  
Author(s):  
Elías Castellanos ◽  
Celia Escamilla-Rivera ◽  
Claus Lämmerzahl ◽  
Alfredo Macías
Keyword(s):  
Scalar Field ◽  
Field Configuration ◽  
Einstein Condensate ◽  
De Sitter ◽  
Bose Einstein Condensate ◽  
Sitter Spacetime ◽  
Sitter Background ◽  
The Stability ◽  
Bose Einstein ◽  
Natural Way

In this paper, we analyze some properties of a scalar field configuration, where it is considered as a trapped Bose–Einstein condensate in a Schwarzschild–de Sitter background spacetime. In a natural way, the geometry of the curved spacetime provides an effective trapping potential for the scalar field configuration. This allows us to explore some thermodynamical properties of the system. Additionally, the curved geometry of the spacetime also induces a position-dependent self-interaction parameter, which can be interpreted as a kind of gravitational Feshbach resonance, that could affect the stability of the cloud and could be used to obtain information about the interactions among the components of the system.

scholarly journals Stability of logarithmic Bose–Einstein condensate in harmonic trap

2015 ◽  
Vol 29 (01) ◽  
pp. 1450260 ◽  
Author(s):  
Brahim Bouharia
Keyword(s):  
Equations Of Motion ◽  
Numerical Data ◽  
Einstein Condensate ◽  
Harmonic Trap ◽  
Bose Einstein Condensate ◽  
Characteristic Features ◽  
Collective Oscillations ◽  
The Stability ◽  
Three Body ◽  
Bose Einstein

In this paper, we investigate the stability of a recently introduced Bose–Einstein condensate (BEC) which involves logarithmic interaction between atoms. The Gaussian variational approach is employed to derive equations of motion for condensate widths in the presence of a harmonic trap. Then we derive the analytical solutions for these equations and find them to be in good agreement with numerical data. By analyzing deeply the frequencies of collective oscillations, and the mean-square radius, we find that the system is always stable for both negative and positive week logarithmic coupling. However, for strong interaction the situation is quite different: Our condensate collapses for positive coupling and oscillates with fixed frequency for negative one. These special results remain the most characteristic features of the logarithmic BEC compared to that involving two-body and three-body interactions.

STABILITY OF BOSE–EINSTEIN CONDENSATES IN A LORENTZ VIOLATING SCENARIO

2010 ◽  
Vol 25 (06) ◽  
pp. 459-469 ◽  
Author(s):  
E. CASTELLANOS ◽  
A. CAMACHO
Keyword(s):  
Nonlinear Term ◽  
Scattering Length ◽  
Lorentz Violation ◽  
Einstein Condensate ◽  
Pitaevskii Equation ◽  
Quantum Structure ◽  
Bose Einstein Condensate ◽  
The Stability ◽  
The One ◽  
Bose Einstein

We analyze the stability of a Bose–Einstein condensate in a Lorentz violating scenario, which is characterized by a deformation in the dispersion relation. The incorporation of a Lorentz violation within the bosonic statistics has, as a consequence, the emergence of a pseudo-interaction, the one can be associated to a characteristic scattering length. In addition, we calculate the relevant parameters associated to the stability of such condensate incorporating this pseudo-interaction in the nonlinear term of the Gross–Pitaevskii equation. We show that these parameters must be corrected, as a consequence of the quantum structure of spacetime.

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