Separating particles according to their physical properties: Transverse drift of underdamped and overdamped interacting particles diffusing through two-dimensional ratchets

We study the transverse net current of particles moving through two-dimensional (2D) square arrays or chains of potential energy hills or wells when driven perpendicularly to their spatial symmetry axis (i.e., the mirror-symmetry axis). This transverse rectification is quite general and occurs for nonzero inertia, and/or interaction, and/or temperature. We separately consider both cases: underdamped and overdamped interacting particles. The interplay between inertia and thermal fluctuations, no matter how weak, determines robust rectification properties, that allow distinct control techniques for transport of underdamped (e.g., electrons or colloids) versus overdamped particles (e.g., vortices) in asymmetric nanodevices and microdevices. Furthermore, 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 particle separation devices.