Dynamics of rotating two-component Bose–Einstein condensates and its efficient computation

Zhang, Yanzhi; Bao, Weizhu; Li, Hailiang

doi:10.1016/j.physd.2007.06.026

Cited by 53 publications

(82 citation statements)

References 50 publications

(87 reference statements)

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“…For the completeness and convenience of the readers, here we also present some numerical results for the dynamics of rotating two-component BEC [53]. For more numerical results, one can refer to [4,9,53].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…For more numerical results, one can refer to [4,9,53]. The problem is solved numerically on a bounded computational domain Ω x = {(x, y), r = x 2 + y 2 < R} with R = 12 by the numerical method in the previous section and we choose mesh sizes ∆r = 0.005, ∆θ = π/128 and time step ∆t = 0.0001.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The problem is solved numerically on a bounded computational domain Ω x = {(x, y), r = x 2 + y 2 < R} with R = 12 by the numerical method in the previous section and we choose mesh sizes ∆r = 0.005, ∆θ = π/128 and time step ∆t = 0.0001. Figure 1 [53] shows the time evolution of density of each component for two sets of interaction parameters: (i) β 11 = β 12 = β 22 = 500 (i.e. a 11 : a 12 : a 22 = 1 : 1 : 1); (ii) β 11 = 500, β 12 = 300 and β 22 = 400 (i.e.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Proof: Again, the proof follows the line of the analogous result for the case of κ 1 = κ 2 = 0 in [53]. .2) is chosen as a stationary state with a shift in its center, one can construct an exact solution of the CGPEs (2.1) with harmonic oscillator potentials (2.4).…”

Section: )) Is the Solution Of Problem (21)-(22); Then We Havementioning

confidence: 89%

“…For the convenience of the reader, here we review a method which discretizes the equation (4.15) in the θ-direction by the Fourier pseudospectral method, in the r-direction by the fourth-order finite difference method, in the zdirection by the sine pseudospectral method and in time by the Crank-Nicolson (C-N) scheme [5,53]. In order to do so, we choose the bounded computational domain Ω x = {(x, y), r = x 2 + y 2 < R} in 2D, and resp.…”

Section: Methodsmentioning

confidence: 99%

See 4 more Smart Citations

Analysis and efficient computation for the dynamics of two-component Bose-Einstein condensates

Bao¹

2008

Stationary and Time Dependent Gross-Pitaevskii Equations

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Abstract. In this paper, we review some recent results on the analysis and efficient computation for the dynamics of rotating two-component Bose-Einstein condensates (BECs). We begin with the three-dimensional (3D) coupled GrossPitaevskii equations (GPEs) with an angular momentum rotation term and an external driving field, show how to scale it into dimensionless form, reduce it to a 2D and 1D GPE in the limiting regime of strong anisotropic confinement and present its semiclassical scaling and geometric optics. Dynamic laws on the angular momentum expectation, density of each component, condensate widths and analytical solutions of stationary states with its center shifted from the trapping center are presented. In addition, efficient and accurate numerical methods for computing the dynamics of rotating two-component BEC are presented and some numerical results are reported to demonstrate the efficiency and accuracy of the numerical methods.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: )) Is the Solution Of Problem (21)-(22); Then We Havementioning

confidence: 89%

Section: Methodsmentioning

confidence: 99%

See 3 more Smart Citations

Analysis and efficient computation for the dynamics of two-component Bose-Einstein condensates

Bao¹

2008

Stationary and Time Dependent Gross-Pitaevskii Equations

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A linearized, decoupled, and energy‐preserving compact finite difference scheme for the coupled nonlinear Schrödinger equations

Wang

2016

Numerical Methods Partial

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In this article, a decoupled and linearized compact finite difference scheme is proposed for solving the coupled nonlinear Schrödinger equations. The new scheme is proved to preserve the total mass and energy which are defined by using a recursion relationship. Besides the standard energy method, an induction argument together with an H1 technique are introduced to establish the optimal point‐wise error estimate of the proposed scheme. Without imposing any constraints on the grid ratios, the convergence order of the numerical solution is proved to be of O ( h 4 + τ 2 ) with mesh size h and time step τ. Numerical results are reported to verify the theoretical analysis, and collision of two solitary waves are also simulated. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 840–867, 2017

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Rotating multicomponent Bose–Einstein condensates

Liu

2011

Nonlinear Differ. Equ. Appl.

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Abstract. In the understanding of the spatial behavior of interacting components of multicomponent Bose-Einstein condensates (BECs), a central problem is to establish whether coexistence of all the components occurs, or the interspecies interaction leads to extinction, that is, configurations where one or more densities are null. In this paper, for the rotating k-mixture BEC, we prove that the interspecies interaction leads to extinction in the Thomas-Fermi approximation. Mathematics Subject Classification (2000). 35B65, 35K55.

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Dynamics of rotating two-component Bose–Einstein condensates and its efficient computation

Cited by 53 publications

References 50 publications

Analysis and efficient computation for the dynamics of two-component Bose-Einstein condensates

Analysis and efficient computation for the dynamics of two-component Bose-Einstein condensates

A linearized, decoupled, and energy‐preserving compact finite difference scheme for the coupled nonlinear Schrödinger equations

Rotating multicomponent Bose–Einstein condensates

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