Emergence of a ratchet motor by spontaneous symmetry breaking

A circular disk without any asymmetry exhibits a one-way spin on a vibrating granular layer. Vertical agitation generates a random motion of particles by mutual collision. A circular disk, placed on the layer with its center fixed, is moved by collision with the particles. After the vibration began, the circular disk exhibits a one-way spin in a stochastic manner. Before the start of the one-way spin, the particles, which were homogeneously distributed under the disk at the initial state, spontaneously gather on one side, forming an asymmetric distribution of particles. This asymmetric distribution causes the disk-inclination. Simultaneously, the agitated particles cannot enter the lower part of the inclined disk. Resultantly, the disk-inclination and the asymmetric distribution of particles maintain the situation with stable manner. Then, the inclined disk rotates with the precession movement around this inclined axis. The disk-spin is synchronized with the rotation of the disk-inclination. This phenomenon can be reproduced by a simple mathematical model referring to the precession movement of a spinning top. Though the present system may be regarded as a type of ratchet motor, any asymmetries are not equipped in the initial setup. To the best of our knowledge, this is the first ratchet motor to produce an asymmetric structure in a self-organizing manner.