Diffusion of particles in restricted geometries is a subject of considerable interest due to their applicability in the observation and manipulation of nanoscopic systems. The single-file model has been introduced to model situations where the particles are constrained to move in nanopores in a single file without the chance for a particle exchange. Similarly, the motion of Brownian particles moving in a ratchet potential has been an active area of research because of its applicability to a wide range of nanoscale systems, including the transport properties of molecular motors. Here, we briefly review these models and discuss particle motion in a ratchet model constrained with the single-file condition. The motion of overdamped particles in a single-file model constrained to move in a ratchet potential is subdiffusive with mean square displacement that has t12 time dependence when hard-core interaction is significant, and becomes diffusive for long times. The N-particle switching time for maximum current is N times the switching time for one particle maximum current.

PACS Nos 87.15.Aa, 87.15.Vv, 05.60.Cd, 05.45.Ac