Spectral collocation and a twolevel continuation scheme for dipolar BoseEinstein condensates
Abstract
We exploit the high accuracy of spectral collocation methods in the context of a twolevel continuation scheme for computing ground state solutions of dipolar BoseEinstein condensates (BEC), where the first kind Chebyshev polynomials and Fourier sine functions are used as the basis functions for the trial function space. The governing GrossPitaevskii equation (or Schrödinger equation) can be reformulated as a SchrödingerPoisson (SP) type system [13]. The twolevel continuation scheme is developed for tracing the first solution curves of the SP system, which in turn provide an appropriate initial guess for the Newton method to compute ground state solutions for 3D dipolar BEC. Extensive numerical experiments on 3D dipolar BEC and dipolar BEC in optical lattices are reported.
 Publication:

Journal of Computational Physics
 Pub Date:
 January 2014
 DOI:
 10.1016/j.jcp.2013.09.018
 Bibcode:
 2014JCoPh.256..713J