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02/17/04 Colloquium
DR. WEINZHU BAO
DEPARTMENT OF COMPUTATIONAL SCIENCE
NATIONAL UNIVERSITY OF SINGAPORE
DEPARTMENT OF COMPUTATIONAL SCIENCE
NATIONAL UNIVERSITY OF SINGAPORE
Numerical Simulation for Bose-Einstein Condensation
Abstract: In this talk, we present efficient and stable numerical methods to compute ground states and dynamics of Bose-Einstein condensates (BEC). As preparatory steps, we take the 3rd Gross-Pitaevskii equation (GPE), scale it to obtain a three-parameter model and use an approach well known in the physical literature to reduce it to 2d and 1d GPEs in certain limiting regimes. Two numerical methods are presented to compute the ground and excited states and a time-splitting spectral method is used to solve the time-dependent GPE for dynamics. The numerical methods are applied to study collapse and explosion of BEC, as well as stability and interaction of central vortex states in BEC. Comparison of our numerical results and experiment data are also presented.