Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18120
標題: 可調整的多重網格-延續法處理在週期性位能下的玻色-愛因斯坦凝聚態問題。
Adaptive multigrid-continuation methods for Bose-Einestein condensates in a periodic potential.
作者: 白佶弘
Bai, Ji-Hong
關鍵字: nonlinear Schr&ouml
非線性薛丁格方程
dinger equation
continuation method
two-grid scheme
bifurcation
Bloch waves
延續法
雙重網格法
分歧
布洛赫波
出版社: 應用數學系所
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摘要: 我們利用多重網格延續法處理與參數有關的問題。我們所提出的演算法,是雙重網格離散法的推廣,可以很有彈性的被執行。也就是說,解曲線的近似點並不一定位於相同的細網格上。我們用此演算法計算具有週期位能的玻色-愛因斯坦凝聚態的能階和超流體的密度。若散射長度為正數,且化學能足夠大和定義域適當地被選擇,我們的數值結果顯示出有週期位能的玻色-愛因斯坦凝聚態最初幾個波函數的尖峰數與週期位能的波數有關。此外,若黑暗的孤立子的週期性位能用餘弦函數描述,其基態解的尖峰數目是Π(2l/d_j)個。最後,我們探討兩階段延續法解在光學晶格上有Bloch waves的一維玻色-愛因斯坦凝聚態問題。我們亦對數值試驗的結果提出報告。
We study multigrid-continuation method for treating parameter-dependent problems. The proposed algorithm which can be flexibly implemented is a generalization of the two-grid discretization schemes [8]. That is, approximating points on a solution curve do not necessarily lie on the same fine grid. We apply the algorithm to compute energy levels and superfluid densities of Bose-Einstein condensates (BEC) in a periodic potential. For positive scattering length, if the chemical potential is large enough, and the domain is properly chosen, the results show that the number of peaks of the first few energy states of the 1D BEC and 2D BEC in a periodic potential depends on the wave number of the periodic potential. Moreover, for dark solitons the number of peaks of the ground state solutions is Π(2l/d_j), where the periodic potential is expressed in terms of the cosine functions. Finally, we study two-stage continuation algorithms for Bloch waves of 1D BEC in optical lattices. Our sample numerical result is reported.
URI: http://hdl.handle.net/11455/18120
其他識別: U0005-1905200920594300
文章連結: http://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-1905200920594300
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