Generalized Langevin subdiffusion in channels: The bath always wins

Abstract

We consider subdiffusive motion, modeled by the generalized Langevin equation in an equilibrium setting, of tracer particles in channels of indefinite length in the $x$ direction: the channels of varying width and the channels with sinusoidally meandering midline. The subdiffusion in the $x$ direction is not affected by constraints put by the channel. This is especially astonishing for meandering channels whose centerline might be quite long. The same behavior is seen in a holonomic model of a bead on a sinusoidal and meandering wire, where some analytic insights are possible.