受侷限玻色-愛因斯坦凝聚體中的渦旋環動力學

• Main Author: 薛哲修
• Other Authors: 郭西川
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/45818327044941690559

博士 === 國立彰化師範大學 === 物理學系 === 98 === In the first part, we propose a numerical scheme for obtaining the stationary vortex-ring solutions of the Gross-Pitaevskii (GP) equation for an axisymmetrically trapped Bose-Einstein condensate (BEC). The effective energy functional and the associated GP equation are derived by assuming a trial phase profile for the wavefunction that is subject to the condition of circulation quantization on the rz plane. The wavefunction of the vortex ring is determined by solving the ground state of the effective GP equation numerically. Application of our method to the formation of a three-dimensional Skyrmion in a trapped two-component BEC is demonstrated. By generalizing the technique of generating vortex ring, complex vortex configurations composed of single vortex or many vortices can be obtained, and their dynamical evolutions can also be observed by integrating the GP equation numerically. As a result of this scheme, we investigate the dynamics of an unstable vortex ring in a pancake-shaped BEC by solving the GP equation numerically. It is found that a quasisteady turbulent state with long relaxation time can be achieved through the disruption of a perturbed vortex ring in the condensate owing to the bending-wave instability. We verify that this quantum turbulent state is characterized by Kolmogorov energy spectrum.