作为Kapitzas摆推广的驱动环形螺旋线
Driven toroidal helix as a generalization of Kapitzas pendulum
摘要：
我们探讨了一个模型系统，由一个粒子被限制为沿着一个环形螺旋线移动，同时暴露于一个静态的电位，以及由于一个谐波振荡电场的驱动力。它示出，在一个消失的螺旋半径的限制的运动方程与那些著名的Kapitza摆-一个经典的摆振荡枢轴-这意味着驱动的环形螺旋线表示相应的概括。它表明，两个占主导地位的静态不动点存在于卡皮察摆也存在一个有限的螺旋半径。这两个固定点的螺旋半径，驱动振幅和静态电位的稳定性的依赖关系进行了分析和数值计算。此外，最突出的偏差驱动螺旋从Kapitzas摆相对于所产生的相空间进行了调查和分析的一些细节。这些影响包括一个不寻常的过渡到混沌和有效的定向运输由于同时存在多个混沌相空间区域。
英文摘要：
We explore a model system consisting of a particle confined to move along a toroidal helix while being exposed to a static potential as well as a driving force due to a harmonically oscillating electric field. It is shown that in the limit of a vanishing helix radius the governing equations of motion coincide with those of the well-known Kapitza pendulum - a classical pendulum with oscillating pivot - implying that the driven toroidal helix represents a corresponding generalization. It is shown that the two dominant static fixed points present in the Kapitza pendulum are also present for a finite helix radius. The dependence of the stability of these two fixed points on the helix radius, the driving amplitude, and the static potential are analyzed both analytically and numerically. Additionally, the most prominent deviations of the driven helix from Kapitzas pendulum with respect to the resulting phase space are investigated and analyzed in some detail. These effects include an unusual transition to chaos and an effective directed transport due to the simultaneous presence of multiple chaotic phase space regions.
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