Rotational diffusion of a molecular cat: Fractional statistics in the harmonic three-body problem

We study the non-holonomic rotational dynamics of the classical harmonic three mass system in the strongly nonlinear regime. This is the simplest isolated spring-mass model capable of displaying rotation with zero angular momentum as well as chaotic dynamics. Combined together these two phenomena lead to a wide variety of qualitatively distinct dynamical phases as a function of the system's internal energy. 
For low energy, where dynamics are regular, we observe a constant rotation rate with zero angular momentum. For sufficiently high energy we observe a rotational random walk driven by the system's internal chaotic dynamics. For intermediate energies, we observe ballistic bouts of constant rotation rates interrupted by unpredictable orientation reversal events. In this regime, the system constitutes a simple physical model for Levy walks and the orientation reversal statistics lead to fractional rotational diffusion interpolating smoothly between the ballistic and regular diffusive regimes.