Bulk-mediated surface diffusion along a cylinder: Propagators and crossovers

We consider the effective motion along a cylinder of a particle that freely diffuses in the bulk and intermittently binds to the cylinder. From an exact approach we derive the different regimes of the effective motion along the cylinder characterized by physical rates for binding/unbinding and the bulk diffusivity. We obtain a transient regime of superdiffusion and, interestingly, a saturation regime characteristic for the cylindrical geometry. This saturation in a finite system is not terminal but eventually turns over to normal diffusion along the cylinder. The first passage behavior of particles to the cylinder surface is derived. Consequences for actual systems are discussed.