论文标题
驱动的环形螺旋作为kapitzas pendulum的概括
Driven toroidal helix as a generalization of Kapitzas pendulum
论文作者
论文摘要
我们探索了一个模型系统，该模型系统由局限于沿环形螺旋的粒子组成，同时暴露于静态电势以及由于谐波振荡电场而导致的驱动力。结果表明，在消失的螺旋半径的极限中，运动的运动方程与众所周知的Kapitza pendulum（具有振动枢轴的经典摆动）一致，这意味着驱动的环螺旋螺旋代表相应的普遍性。结果表明，对于有限的螺旋半径也存在Kapitza摆中存在的两个主要静态固定点。通过分析和数值分析，这两个固定点在螺旋半径上的稳定性，驱动幅度和静态电势的依赖性。此外，研究和分析了驱动的螺旋与卡皮扎斯摆的最突出的偏差相对于所得的相空间。这些影响包括异常过渡到混乱，以及由于同时存在多个混沌相空间区域而导致有效的定向运输。
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.
