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arXiv 0802.4055quant-phnlin.CD
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偶极气体玻色-爱因斯坦凝聚中的分岔、有序和混沌

Bifurcations, order, and chaos in the Bose-Einstein condensation of dipolar gases

Patrick Köberle, Holger Cartarius, Tomaž Fabčič, Jörg Main, Günter Wunner

摘要:

我们应用变分技术来解决的玻色-爱因斯坦凝聚体,其中一个额外的偶极-偶极原子之间的相互作用是目前与建模的目标,这种凝聚体的动力学的Gross-Pitaevskii方程。我们发现,通用的稳定阈值的凝聚体的崩溃对应的分岔点,总是两个固定的解决方案的Gross-Pitaevskii方程消失在切线分岔,一个动态稳定和其他不稳定。我们指出,阈值也对应于“例外点”,即分支奇点的哈密顿量。我们分析了动力学的激发凝聚体波函数通过庞加莱表面的凝聚体参数的截面,并找到规则和混乱的运动,分别对应于(准)周期振荡和不规则波动的凝聚体。稳定的岛屿被发现坚持到能量远高于鞍点的平均场能量,旁边的崩溃模式。当凝聚体的形状为轴对称时,这些结果是适用的。

英文摘要:

We apply a variational technique to solve the time-dependent Gross-Pitaevskii equation for Bose-Einstein condensates in which an additional dipole-dipole interaction between the atoms is present with the goal of modelling the dynamics of such condensates. We show that universal stability thresholds for the collapse of the condensates correspond to bifurcation points where always two stationary solutions of the Gross-Pitaevskii equation disappear in a tangent bifurcation, one dynamically stable and the other unstable. We point out that the thresholds also correspond to "exceptional points," i.e. branching singularities of the Hamiltonian. We analyse the dynamics of excited condensate wave functions via Poincare surfaces of section for the condensate parameters and find both regular and chaotic motion, corresponding to (quasi-) periodically oscillating and irregularly fluctuating condensates, respectively. Stable islands are found to persist up to energies well above the saddle point of the mean-field energy, alongside with collapsing modes. The results are applicable when the shape of the condensate is axisymmetric.

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