Controlling the motion of interacting particles: homogeneous systems and binary mixtures

We elaborate on recent results on the transport of interacting particles for both single-species and binary mixtures subject to an external driving on a ratchetlike asymmetric substrate. Moreover, we also briefly review motion control without any spatial asymmetric potential (i.e., no ratchet). Our results are obtained using an analytical approach based on a nonlinear Fokker-Planck equation as well as via numerical simulations. By increasing the particle density, the net dc ratchet current in our alternating (ac)-driven systems can either increase or decrease depending on the temperature, the drive amplitude, and the nature of the inter-particle interactions. This provides an effective control of particle motion by just changing the particle density. At low temperatures, attracting particles can condense at some potential minima, thus breaking the discrete translational symmetry of the substrate. Depending on the drive amplitude, an agglomeration or condensation results either in a drop to zero or in a saturation of the net particle velocity at densities above the condensation density-the latter case producing a very efficient rectification mechanism. For binary mixtures we find three ways of controlling the particle motion of one (passive) B species by means of another (active) A species: (i) Dragging the target particles B by driving the auxiliary particles A, (ii) rectifying the motion of the B particles on the asymmetric potential created by the A-B interactions, and (iii) dynamically modifying (pulsating) this potential by controlling the motion of the A particles. This allows to easily control the magnitude and direction of the velocity of the target particles by changing either the frequency, phase and/or amplitude of the applied ac drive(s).