Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
Phys Rev Lett. 2019 Jan 18;122(2):024102. doi: 10.1103/PhysRevLett.122.024102.
In flat space, changing a system's velocity requires the presence of an external force. However, an isolated nonrigid system can freely change its orientation due to the nonholonomic nature of the angular momentum conservation law. Such nonrigid isolated systems may thus manifest their internal dynamics as rotations. In this work, we show that for such systems chaotic internal dynamics may lead to macroscopic rotational random walk resembling thermally induced motion. We do so by studying the classical harmonic three-mass system in the strongly nonlinear regime, the simplest physical model capable of zero angular momentum rotation as well as chaotic dynamics. At low energies, the dynamics are regular and the system rotates at a constant rate with zero angular momentum. For sufficiently high energies a rotational random walk is observed. For intermediate energies the system performs ballistic bouts of constant rotation rates interrupted by unpredictable orientation reversal events, and the system constitutes a simple physical model for Lévy walks. The orientation reversal statistics in this regime lead to a fractional rotational diffusion that interpolates smoothly between the ballistic and regular diffusive regimes.
在平坦空间中，改变系统的速度需要外力的存在。然而，由于角动量守恒定律的非完整性质，孤立的非刚性系统可以自由地改变其方向。因此，这种非刚性孤立系统可能会将其内部动力学表现为旋转。在这项工作中，我们表明，对于这种系统，混沌的内部动力学可能导致类似于热诱导运动的宏观旋转随机游动。我们通过研究强非线性 regime 下的经典谐波三体系统来做到这一点，这是最简单的物理模型，能够实现零角动量旋转和混沌动力学。在低能量下，动力学是规则的，系统以零角动量以恒定速率旋转。对于足够高的能量，会观察到旋转随机游动。在中间能量下，系统会进行恒定旋转速率的弹道爆发，中间会有不可预测的方向反转事件，系统构成了 Lévy 游走的简单物理模型。该 regime 中的方向反转统计数据导致分数旋转扩散，在弹道和规则扩散 regime 之间平滑插值。
