Separating particles according to their physical properties: Transverse drift of over-damped interacting particles through two-dimensional ratchets

We study the transverse net current of particles moving through two-dimensional square arrays or chains of potential energy hills or wells when driven perpendicularly to their spatial symmetry axis (i.e., the mirror-symmetry axis). Although unrelated to the usual Hall effect, such a zero-applied-magnetic-field Hall-like particle current can be observed for vortices, electrons, colloidal particles, and other interacting particles. This effect is quite general and occurs for non-zero inertia, and/or interaction, and/or temperature. We focus on two-dimensional ratchets and we also study the transverse rectification with particle interactions. The transverse rectification of interacting particles moving through 2D asymmetric potential landscapes can drop to zero if their interaction length is smaller than a certain characteristic geometric length. This size-selective rectification mechanism could be used for developing new particle separation devices. Ratchets of interacting particles could also be used to separate these based on either their spin, mass, or charge.