Symmetry of Brownian Photomotors

The symmetry conditions under which the ratchet effect of a Brownian photomotor occurs or does not occur were considered. Using symmetry transformations for which average photomotor velocity is invariant, it was shown that, on substrates with symmetric charge distribution, individual Brownian particles can undergo directed motion only if an antisymmetric charge distribution fluctuates in them. In this case, the ensemble with averaged orientations of particles cannot execute directed motion as a whole and spreads by diffusion. On the other hand, on substrates with antisymmetric charge distribution, both individual Brownian particles and their ensemble with averaged orientations can undergo directed motion only if a symmetric charge distribution fluctuates. If the time dependence of the particle charge distribution is described by a periodic function of time with a universal type of symmetry (which is simultaneously symmetric, antisymmetric, and invariant under a half-period shift with sign reversal), then the ratchet effect cannot occur in the overdamped regime, but it is allowed if the inertia of particles is taken into account and the charge distributions in both the particle and the substrate are neither symmetric nor antisymmetric.