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Tzyy-Leng Horng

2008-11-26
09:00:00 - 12:00:00

Fourier pseudospectral method on solving the governing equation of Bose-Einstein condensate -- Gross-Pitaevskii equation

405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Fourier pseudospectral method is employed here to solve time-dependent Gross-Pitaevskii equation (GPE) governing non-homogeneous Bose-Einstein condensate (BEC). Here GPE is numerically solved by method of lines (MOL), which discretizes the PDE in space first and then applies well-developed ODE solvers to solve this afterwards semi-discrete ODE system. Currently, GPE is spatially discretized by the spectrally accurate Fourier collocation method with the implied periodic extension of computational domain being justified by the density approaching quiescence rapidly as the radius goes beyond Thomas-Fermi radius. The integration in time is implemented by RK23, a 2nd order ODE solver with tolerance of error control through variable time step. In case of finding the ground state, the integration in time is particularly done through imaginary axis with normalization of density (from the constraint of mass conservation) for every few time steps. In this talk, we will demonstrate several computational results by the current GPE solver, especially our current work – computing the ground state of a two-component BEC under rotation.