Self-Driven Fractional Rotational Diffusion of the Harmonic Three-Mass System

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 Levy walks. The orientation reversal statistics in this regime lead to a fractional rotational diffusion that interpolates smoothly between the ballistic and regular diffusive regimes.