3-Dimensional Simulation of Quantum Vortex in a Bose-Einstein Condensate

1.我们直接积分三维时间相关的Gross-Pitaevskii方程，以检验玻色-爱因斯坦凝聚（BEC）如何在旋转触发下动态变化。我们提出了尚未探索的三维非稳态动力学，包括涡旋起始前的表面波纹，涡旋湍流状态和涡旋晶格状态。为了阐明费米子超流体气体中靠近费什巴赫共振的单量子化涡的结构，我们对玻色子-费米子模型中的广义Bogoliubov-de Gennes方程进行了数值求解。给出了超流费米子气体中单涡旋的详细性质。通过求解Gross-Pitaevskii方程，对超流体湍流的能谱进行了数值研究。得到的能谱与Kolmogorov低相一致。

1.We directly integrate the 3-D time-dependent Gross-Pitaevskii equation in order to examine how Bose-Einstein condensate (BEC) dynamically changes by a trigger of the rotation. We present unexplored 3-D non-steady dynamics including the surface ripples preceding vortex initiations, the vortex turbulent state and the vortex lattice state.2.In order to clarify the structure of a single quantized vortex in a superfluid fermion gas near the Feshbach resonance, we numerically solve the generalized Bogoliubov-de Gennes equation in the boson-fermion model. We present detailed properties of single vortex in a superfluid fermion gas.3.The energy spectrum of superfluid turbulence is studied numerically by solving the Gross-Pitaevskii equation. The obtained energy spectrum is consistent with the Kolmogorov low.