Soliton ratchet induced by random transitions among symmetric sine-Gordon potentials

Abstract

The generation of net solitonmotion induced by randomtransitions among N symmetric phase-shifted sine-Gordon potentials is investigated, in the absence of any external force and without any thermal noise. The phase shifts of the potentials and the damping coe cients depend on a stationary Markov process. Necessary conditions for the existence of transport are obtained by an exhaustive study of the symmetries of the stochastic system and of the soliton velocity. It is shown that transport is generated by unequal transfer rates among the phase-shifted potentials or by unequal friction coe cients or by a properly devised combination of potentials (N > 2). Net motion and inversions of the currents, predicted by the symmetry analysis, are observed in simulations as well as in the solutions of a collective coordinate theory. A model with high e cient solitonmotion is designed by usingmultistate phase-shifted potentials and by breaking the symmetrieswith unequal transfer rates.