Numerical Studies of Rotating Bose-Einstein Condensates via Rotating Lagrangian Coordinates

Abstract

In this thesis, the dynamics of rotating Bose-Einstein Condensation is studied. Under a new Lagrangian coordinate system, the analytical form of density, energy, angular momentum expectation, condensate width and the centre of mass are redefined. The conservation of density, energy and the angular momentum expectation are proved when the trapping potential is radially symmetric in 2D. Then, a second order time splitting method and Fourier pseudo spectral method in space are applied to study numerically the dynamics of condensate. Extensive numerical experiments are done to demonstrate the dynamic results.