Rotational random walk of the harmonic three body system

Abstract

When Robert Brown first observed colloidal pollen grains in water he inaccurately concluded that their motion arose "neither from currents in the fluid, nor from its gradual evaporation, but belonged to the particle itself". In this work we study the dynamics of a classical molecule consisting of three masses and three harmonic springs in free space that does display a rotational random walk "belonging to the particle itself". The geometric nonlinearities arising from the non-zero rest lengths of the springs connecting the masses break the integrability of the harmonic system and lead to chaotic dynamics in many regimes of phase space. The non-trivial connection of the system's shape space allows it, much like falling cats, to rotate with zero angular momentum and manifest its chaotic dynamics as an orientational random walk. In the transition to chaos the system displays random orientation reversals and provides a simple realization of Lévy walks.

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Cited by in corpus (11)

• Regular Regimes of the Three Body Harmonic System
• Universality in the Onset of Super-Diffusion in Lévy Walks
• Fractional and scaled Brownian motion on the sphere: The effects of long-time correlations on navigation strategies
• Intrinsic Attractive and Repulsive Interactions: From Classical to Quantum Gases in the Generalized Maxwell-Boltzmann Distribution
• Nonlinear dynamics and emergent statistical regularity in classical Lennard-Jones three-body system upon disturbance
• Mittag-Leffler Quantum Statistics and Thermodynamic Anomalies
• 3-body harmonic molecule
• Classical $n$-body system in volume variables. II. Four-body case
• Stochastic Dissipative Euler's equations for a free body
• Emergent dynamic stress regulators via coordinated thermal fluctuations and stress in harmonic crystalline lattices
• A molecular dynamics simulation of thermalization of crystalline lattice with harmonic interaction