scholarly journals A Convergent Three-Step Numerical Method to Solve a Double-Fractional Two-Component Bose–Einstein Condensate

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1412
Author(s):  
Adán J. Serna-Reyes ◽  
Jorge E. Macías-Díaz ◽  
Nuria Reguera
Keyword(s):  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Einstein Condensate ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Nonlinear Parabolic ◽  
Complex Functions ◽  
Two Component ◽  
The One ◽  
Bose Einstein

This manuscript introduces a discrete technique to estimate the solution of a double-fractional two-component Bose–Einstein condensate. The system consists of two coupled nonlinear parabolic partial differential equations whose solutions are two complex functions, and the spatial fractional derivatives are interpreted in the Riesz sense. Initial and homogeneous Dirichlet boundary data are imposed on a multidimensional spatial domain. To approximate the solutions, we employ a finite difference methodology. We rigorously establish the existence of numerical solutions along with the main numerical properties. Concretely, we show that the scheme is consistent in both space and time as well as stable and convergent. Numerical simulations in the one-dimensional scenario are presented in order to show the performance of the scheme. For the sake of convenience, A MATLAB code of the numerical model is provided in the appendix at the end of this work.

scholarly journals Control of anomalous diffusion of a Bose polaron

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 232
Author(s):  
Christos Charalambous ◽  
Miguel Ángel García-March ◽  
Gorka Muñoz-Gil ◽  
Przemysław Ryszard Grzybowski ◽  
Maciej Lewenstein
Keyword(s):  
Anomalous Diffusion ◽  
Coupling Strength ◽  
Rabi Frequency ◽  
Einstein Condensate ◽  
The Other ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Coherent Coupling ◽  
Two Component ◽  
Bose Einstein

We study the diffusive behavior of a Bose polaron immersed in a coherently coupled two-component Bose-Einstein Condensate (BEC). We assume a uniform, one-dimensional BEC. Polaron superdiffuses if it couples in the same manner to both components, i.e. either attractively or repulsively to both of them. This is the same behavior as that of an impurity immersed in a single BEC. Conversely, the polaron exhibits a transient nontrivial subdiffusive behavior if it couples attractively to one of the components and repulsively to the other. The anomalous diffusion exponent and the duration of the subdiffusive interval can be controlled with the Rabi frequency of the coherent coupling between the two components, and with the coupling strength of the impurity to the BEC.

Sonic horizon formation for coupled one-dimensional Bose–Einstein condensate in an elongated harmonic potential

2018 ◽  
Vol 32 (29) ◽  
pp. 1850352
Author(s):  
Ying Wang ◽  
Shuyu Zhou
Keyword(s):  
Expansion Method ◽  
Einstein Condensate ◽  
Wave Functions ◽  
Harmonic Potential ◽  
Pitaevskii Equation ◽  
Two Component System ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Two Component ◽  
Bose Einstein

We theoretically studied the sonic horizon formation problem for coupled one-dimensional Bose–Einstein condensate trapped in an external elongated harmonic potential. Based on the coupled (1[Formula: see text]+[Formula: see text]1)-dimensional Gross–Pitaevskii equation and F-expansion method under Thomas–Fermi formulation, we derived analytical wave functions of a two-component system, from which the sonic horizon’s occurrence criteria and location were derived and graphically demonstrated. The theoretically derived results of sonic horizon formation agree pretty well with that from the numerically calculated values.

Exact Chirped Soliton Solutions for the One-Dimensional Gross– Pitaevskii Equation with Time-Dependent Parameters

2012 ◽  
Vol 67 (3-4) ◽  
pp. 141-146 ◽  
Author(s):  
Zhenyun Qina ◽  
Gui Mu
Keyword(s):  
Soliton Solution ◽  
Soliton Solutions ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Pitaevskii Equation ◽  
Zero Temperature ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
The One ◽  
Bose Einstein

The Gross-Pitaevskii equation (GPE) describing the dynamics of a Bose-Einstein condensate at absolute zero temperature, is a generalized form of the nonlinear Schr¨odinger equation. In this work, the exact bright one-soliton solution of the one-dimensional GPE with time-dependent parameters is directly obtained by using the well-known Hirota method under the same conditions as in S. Rajendran et al., Physica D 239, 366 (2010). In addition, the two-soliton solution is also constructed effectively

Exact breather solutions of repulsive Bose atoms in a one-dimensional harmonic trap

2018 ◽  
Vol 29 (10) ◽  
pp. 1850100
Author(s):  
Ze Cheng
Keyword(s):  
Mean Field Theory ◽  
Mean Field ◽  
Einstein Condensate ◽  
Harmonic Trap ◽  
Number Density ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Surface Plot ◽  
The One ◽  
Bose Einstein

Bose–Einstein condensates of repulsive Bose atoms in a one-dimensional harmonic trap are investigated within the framework of a mean field theory. We solve the one-dimensional nonlinear Gross–Pitaevskii (GP) equation that describes atomic Bose–Einstein condensates. As a result, we acquire a family of exact breather solutions of the GP equation. We numerically calculate the number density [Formula: see text] of atoms that is associated with these solutions. The first discovery of the calculation is that at the instant of the saddle point, the density profile exhibits a sharp peak with extremely narrow width. The second discovery of the calculation is that in the center of the trap ([Formula: see text] m), the number density is a U-shaped function of the time [Formula: see text]. The third discovery of the calculation is that the surface plot of the density [Formula: see text] likes a saddle surface. The fourth discovery of the calculation is that as the number [Formula: see text] of atoms increases, the Bose–Einstein condensate in a one-dimensional harmonic trap becomes stabler and stabler.

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