Name
Title | ||
|---|---|---|
Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates |
Abstract | ||
|---|---|---|
New efficient and accurate numerical methods are proposed to compute ground states and dynamics of dipolar Bose-Einstein condensates (BECs) described by a three-dimensional (3D) Gross-Pitaevskii equation (GPE) with a dipolar interaction potential. Due to the high singularity in the dipolar interaction potential, it brings significant difficulties in mathematical analysis and numerical simulations of dipolar BECs. In this paper, by decoupling the two-body dipolar interaction potential into short-range (or local) and long-range interactions (or repulsive and attractive interactions), the GPE for dipolar BECs is reformulated as a Gross-Pitaevskii-Poisson type system. Based on this new mathematical formulation, we prove rigorously existence and uniqueness as well as nonexistence of the ground states, and discuss the existence of global weak solution and finite time blow-up of the dynamics in different parameter regimes of dipolar BECs. In addition, a backward Euler sine pseudospectral method is presented for computing the ground states and a time-splitting sine pseudospectral method is proposed for computing the dynamics of dipolar BECs. Due to the adoption of new mathematical formulation, our new numerical methods avoid evaluating integrals with high singularity and thus they are more efficient and accurate than those numerical methods currently used in the literatures for solving the problem. Extensive numerical examples in 3D are reported to demonstrate the efficiency and accuracy of our new numerical methods for computing the ground states and dynamics of dipolar BECs. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.jcp.2010.07.001 | J. Comput. Physics |
Keywords | Field | DocType |
efficient numerical method,backward euler sine pseudospectral method,new mathematical formulation,dipolar becs,gross–pitaevskii–poisson type system,time-splitting sine pseudospectral method,dipolar bose-einstein condensate,ground state,new numerical method,dipolar interaction potential,gross-pitaevskii-poisson type system,dipolar bose–einstein condensate,time-splitting sine pseudospectral method.,accurate numerical method,high singularity,gross-pitaevskii equation,extensive numerical example,gross–pitaevskii equation,two-body dipolar interaction potential,dipolar in- teraction potential,type system,three dimensional,pseudospectral method,bose einstein condensate,mathematical analysis,numerical simulation,numerical method | Gross–Pitaevskii equation,Bose–Einstein condensate,Singularity,Weak solution,Spectral method,Numerical analysis,Classical mechanics,Backward Euler method,Mathematics,Pseudo-spectral method | Journal |
Volume | Issue | ISSN |
229 | 20 | Journal of Computational Physics |
Citations | PageRank | References |
15 | 1.15 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Weizhu Bao | 1 | 638 | 95.92 |
| Yongyong Cai | 2 | 80 | 11.43 |
| Hanquan Wang | 3 | 102 | 11.88 |