非对称势阱中快速旋转的玻色-爱因斯坦凝聚
Fast rotating Bose-Einstein condensates in an asymmetric trap
摘要：
我们研究了谐波陷阱的各向异性对快速旋转玻色-爱因斯坦凝聚行为的影响。这是在2D Gross-Pitaevskii方程的框架中完成的，并且需要定义能量的二次型的辛约化。这种约化使我们能够简化巴格曼空间上的能量，并研究大旋转速度的渐近性。我们表征两个制度的速度和各向异性;在第一个的行为是类似的各向同性的情况下，我们构建了一个上界：一个六边形的Abrikosov晶格的旋涡，倒抛物线的轮廓。第二个政权处理非常大的速度，在这种情况下，我们证明，基态不显示在散装涡，与一维限制问题。在这种情况下，我们表明，粗粒原子密度的行为就像一个倒抛物线与大半径的取消限制的方向，但保持一个固定的轮廓由高斯在其他方向。这第二种制度的特征表现为新的现象。
英文摘要：
We investigate the effect of the anisotropy of a harmonic trap on the behaviour of a fast rotating Bose-Einstein condensate. This is done in the framework of the 2D Gross-Pitaevskii equation and requires a symplectic reduction of the quadratic form defining the energy. This reduction allows us to simplify the energy on a Bargmann space and study the asymptotics of large rotational velocity. We characterize two regimes of velocity and anisotropy; in the first one where the behaviour is similar to the isotropic case, we construct an upper bound: a hexagonal Abrikosov lattice of vortices, with an inverted parabola profile. The second regime deals with very large velocities, a case in which we prove that the ground state does not display vortices in the bulk, with a 1D limiting problem. In that case, we show that the coarse grained atomic density behaves like an inverted parabola with large radius in the deconfined direction but keeps a fixed profile given by a Gaussian in the other direction. The features of this second regime appear as new phenomena.
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