scholarly journals A Time-Splitting and Sine Spectral Method for Dynamics of Dipolar Bose-Einstein Condensate

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Si-Qi Li ◽  
Xiang-Gui Li ◽  
Dong-Ying Hua
Keyword(s):  
Spectral Method ◽  
Dipole Interaction ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Three Dimension ◽  
S Wave ◽  
Bose Einstein Condensate ◽  
Two Component ◽  
Time Splitting ◽  
Bose Einstein

A two-component Bose-Einstein condensate (BEC) described by two coupled a three-dimension Gross-Pitaevskii (GP) equations is considered, where one equation has dipole-dipole interaction while the other one has only the usual s-wave contact interaction, in a cigar trap. The time-splitting and sine spectral method in space is proposed to discretize the time-dependent equations for computing the dynamics of dipolar BEC. The singularity in the dipole-dipole interaction brings significant difficulties both in mathematical analysis and in numerical simulations. Numerical results are given to show the efficiency of this method.

scholarly journals Modulation Instability in Two Component Bose-Einstein Condensate with Dissipation

2019 ◽  
Keyword(s):  
Modulation Instability ◽  
Einstein Condensate ◽  
Dissipative Function ◽  
Positive Interaction ◽  
Friction Forces ◽  
Bose Einstein Condensate ◽  
First Case ◽  
Two Component ◽  
Repulsive Forces ◽  
Bose Einstein

In this paper, we consider the dynamic evolution of a binary mixture of a Bose-Einstein condensate taking into account the presence of dissipation inside the components. Using the introduction of the dissipative function, the modified Gross-Pitaevskii equations are obtained. These equations, in contrast to the usual Gross-Pitaevskii equations for two-component condensate, allow us to take into account the dissipation in the system. The influence of dissipative processes on the development of modulation instability in a spatially homogeneous two-component Bose-Einstein condensate is investigated. In contrast to the one-component Bose-Einstein condensate, in which modulation instability arises only when there are forces of attraction between atoms, in a two-component Bose-Einstein condensate nonlinear dynamics, leading to modulation instability is more complex. It essentially depends on the signs and values of the constant interaction of the components, which leads to a greater variety of possible scenarios for the development of modulation instability. The paper considers two cases. The first case is when repulsive forces act inside the components, and the second is when repulsive forces act in the first component, and in the second one - attractive forces. At the same time, the situation when there is a repulsion in the first component, and attraction between the particles in the second component differs significantly from the case of only positive interaction inside the components. The relations between the interaction constants that determine the development of the modulation instability turn out to be different. Given the relations between the interaction constants, taking into account dissipation processes, the occurrence of modulation instability in two-component Bose-Einstein condensates was studied, the maximum growth rate of oscillations was found, and the limits of the existence of modulation instability in the space of wave numbers were found. It is shown that the small effect of dissipation on the modulation instability in the Bose – Einstein condensate is explained not only by the smallness of the friction forces. For wave vectors corresponding to a mode with a maximum increment, the contribution of dissipation in the linear approximation with respect to the dissipative parameter is strictly zero. Thus, the condition for the development of the most rapidly growing mode of oscillations, which determines the beginning of the modulation instability, remains the same as in the nondissipative case.

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