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Title: Quantized vortex states and dynamics for Bose-Einstein condensates
Keywords: Bose-Einstein condensate, Gross-Pitaevskii Equation, Time Splitting Spectral Method, Gradient Flow with Discrete Normalization
Issue Date: 19-Jul-2006
Citation: WANG HANQUAN (2006-07-19). Quantized vortex states and dynamics for Bose-Einstein condensates. ScholarBank@NUS Repository.
Abstract: In this thesis, we analytically and numerically study quantized vortex states as well as their dynamics in rotating Bose-Einstein condensate at extremely low temperature.We present an efficient method--gradient flow with discrete normalization to find the stationary solutions of the Gross-Pitaevskii equation and coupled Gross-Pitaevskii equations.We give a mathematical justification for the correctness of the method. Based on these solutions, we obtain the equilibrium properties such as quantized vortex states of trapped Bose-Einstein condensated gases under rotation at extremely low temperature.We also present a new, efficient and spectrally accurate method--time-splitting spectral method--to numerically solve the Gross-Pitaevskii equation, coupled Gross-Pitaevskii equations and generalized Gross-Pitaevskii equations. Based on the time-dependent solutions of these equations, we numerically obtain the dynamics of quantized vortex states in rotating one-component Bose-Einstein condensate, two-component Bose-Einstein condensates and spinor Bose-Einstein condensates at extremely low temperature.
Appears in Collections:Ph.D Theses (Open)

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