玻色-爱因斯坦凝聚体中相互作用涡旋的动力学：呼吸自由度的作用
Dynamics of trapped interacting vortices in Bose-Einstein condensates: Role of breathing degree of freedom
摘要：
利用变分原理，研究了在强排斥立方非线性作用下，二维单组分玻色-爱因斯坦凝聚体相互作用涡旋有效理论中呼吸宽度自由度的作用.至于试函数，我们选择两个涡函数的乘积，假设一对相互作用，并采用Padé近似中的每个涡函数的振幅形式，该近似适应涡核的特征。我们得到了相互作用涡核坐标与宽度时间导数耦合的Lagrange方程，并借助于非标准Poisson括号得到了它的Hamilton形式。通过求解Hamilton方程，我们发现快速径向呼吸振荡叠加在较慢的旋转运动的涡核，符合Gross-Pitaevskii方程的数值解。在两个涡旋系统的高能态，呼吸宽度自由度在被踢转子中起着踢踢的作用，产生了海胆针结构的混沌。该变分方法的副产品包括：（1）与电荷相关的对数涡间相互作用乘以一个取决于一对核心位置矢量的标量积的前置因子;（2）与电荷无关的短程排斥涡间相互作用和弹簧力。
英文摘要：
With use of a variational principle, we investigate a role of breathing width degree of freedom in the effective theory of interacting vortices in a trapped single-component Bose-Einstein condensates in 2 dimensions under the strong repulsive cubic nonlinearity. As for the trial function, we choose a product of two vortex functions assuming a pair interaction and employ the amplitude form of each vortex function in the Padé approximation which accommodates a hallmark of the vortex core. We have obtained Lagrange equation for the interacting vortex-core coordinates coupled with the time-derivative of width and also its Hamilton formalism by having recourse to a non-standard Poisson bracket. By solving the Hamilton equation, we find rapid radial breathing oscillations superposed on the slower rotational motion of vortex cores, consistent with numerical solutions of Gross-Pitaevskii equation. In higher-energy states of 2 vortex systems, the breathing width degree of freedom plays role of a kicking in the kicked rotator and generates chaos with a structure of sea-urchin needles. Byproduct of the present variational approach includes: (1) the charge-dependent logarithmic inter-vortex interaction multiplied with a pre-factor which depends on the scalar product of a pair of core-position vectors; (2) the charge-independent short-range repulsive inter-vortex interaction and spring force.
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