|
Abstract
|
Recently, simulating dynamics of Bose-Einstein condensates (BEC) are one of most
interesting subjects in Physics. At extremely low temperature, Bose-Einstein condensates can be modelled by the famous Gross-Pitaevskii equation (GPE) or coupled GPEs or nonlocal GPE. We propose a new time-splitting spectral method for the GPE (or GPEs) and study the vortex dynamics of rotating one-component BEC, rotating two-component BEC, spin-1 BEC, spin-2 BEC and dipolar BEC at a very low temperature. This new numerical method is explicit, unconditionally stable, time reversible, time transverse invariant, and of spectral accuracy in space and second-order accuracy in time. Moreover, it conserves the position density in the discretized level. How to design such a method, and how to apply the method into studying vortex dynamics of BEC will be presented in the talk. The GPE is in fact a kind of nonlinear Schrodinger equations. The presented method in this talk can be helpful to design efficient numerical methods for nonlinear Schrodinger equation and coupled nonlinear Schrodinger equations as well.
|
