Dynamics of vortex clusters is essential for understanding diverse superfluid phenomena. In this paper, we examine the dynamics of vortex quadrupoles in a trapped two-dimensional (2D) Bose-Einstein condensate. We find that the movement of these vortex-clusters fall into three distinct regimes which are fully described by the radial positions of the vortices in a 2D isotropic harmonic trap, or by the major radius (minor radius) of the elliptical equipotential lines decided by the vortex positions in a 2D anisotropic harmonic trap. In the "recombination" and "exchange" regimes the quadrupole structure maintains, while the vortices annihilate each other permanently in the "annihilation" regime. We find that the mechanism of the charge flipping in the "exchange" regime and the disappearance of the quadrupole structure in the "annihilation" regime are both through an intermediate state where two vortex dipoles connected through a soliton ring. We give the parameter ranges for these three regimes in coordinate space for a specific initial configuration and phase diagram of the vortex positions with respect to the Thomas-Fermi radius of the condensate. We show that the results are also applicable to systems with quantum fluctuations for the short-time evolution.
Nonlinear Mixing of Collective Modes in Harmonically Trapped Bose-Einstein Condensates
研究了简谐囚禁的玻色-爱因斯坦凝聚体中四极模和剪刀模之间的非线性混合效应。使用微扰技术结合高斯试验波函数的Gross-Pitaevskii方程的变分方法，我们发现，模式混合选择性地发生。我们的微扰方法有助于获得对最近实验的定性理解[Yamazaki et al.，J. Phys. Soc. Japan 84，44001（2015）]，表现出剪刀模式的拍频现象以及由高位四极模式频率对低位四极模式的调制现象。在二阶处理的非线性模式耦合项，我们的方法预测的所有光谱峰的数值模拟的Gross-Pitaevskii方程。
Density functional theory of a trapped Bose gas with tunable scattering length: from weak-coupling to unitarity
在局域密度近似下，利用密度泛函理论研究了T=0时各向同性谐振子约束下的相互作用玻色气体。能量密度泛函跨越正散射长度的整个范围直到酉状态（无限散射长度），通过拟合最近计算的Monte Carlo体状态方程获得[Phys. Rev. A 89，041602（R）（2014）]。我们比较被困气体的密度分布与MC计算得到的。我们求解含时密度泛函方程，研究了相互作用强度的增加对被困气体的四极和四极振荡频率的影响。我们发现，作为散射长度的函数，呼吸模式显示出非单调的行为。我们还考虑了三体损耗对这种模式的阻尼效应。
