Persistence of uphill anomalous transport in inhomogeneous media

For systems out of equilibrium and subjected to a static bias force it can often be expected that particle transport will usually follow the direction of this bias. However, counterexamples exist where particles exhibit uphill motion (known as absolute negative mobility, ANM), particularly in the case of coupled particles. Examples in single particle deterministic systems are less common. Recently, in one such example, uphill motion was shown to occur for an inertial driven and damped particle in a spatially symmetric periodic potential. The source of this anomalous transport was a combination of two periodic driving signals which together are asymmetric under time reversal. In this paper we investigate the phenomena of ANM for a deterministic particle evolving in a periodic and symmetric potential subjected to an external unbiased periodic driving and nonuniform space-dependent damping. It will be shown that this system exhibits a complicated response behavior as certain control parameters are varied, most notably being enhanced parameter regimes exhibiting ANM as the static bias force is increased. Moreover, the solutions exhibiting ANM are shown to be, at least over intermediate time periods, superdiffusive, in contrast to the solutions that follow the bias where the diffusion is normal.