Numerical and variational solutions of the dipolar Gross-Pitaevskii equation in reduced dimensions

Details Numerical and variational solutions of the dipolar Gross-Pitaevskii equation in reduced dimensions Numerical and variational solutions of the dipolar Gross-Pitaevskii equation in reduced dimensions

2011-11-09

arxiv.org/abs/1111.2272v1

Laser Physics 22 (2012) 813-820

Physics

Condensed Matter

Quantum Gases

7 pages, 4 figures

Scientific paper

10.1134/S1054660X12040135

We suggest a simple Gaussian Lagrangian variational scheme for the reduced time-dependent quasi-one- and quasi-two-dimensional Gross-Pitaevskii (GP) equations of a dipolar Bose-Einstein condensate (BEC) in cigar and disk configurations, respectively. The variational approximation for stationary states and breathing oscillation dynamics in reduced dimensions agrees well with the numerical solution of the GP equation even for moderately large short-range and dipolar nonlinearities. The Lagrangian variational scheme also provides much physical insight about soliton formation in dipolar BEC.

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