Temperature-abnormal diffusivity in tilted periodic potentials

The diffusion of particles in tilted spatially periodic potentials in systems with different friction coefficients $\gamma'$ has been studied in a wide temperature range. It has been shown that temperature-abnormal diffusivity is observed in a certain force interval in systems where $\gamma' < 1.1$. In the case of temperature-abnormal diffusivity, the diffusion coefficient $D$ increases with decreasing temperature. At the same time, temperature-abnormal diffusivity is absent at large friction coefficients $\gamma'$ and diffusion is always enhanced with increasing temperature. It has been analyzed how the anomalous temperature dependence of the diffusion coefficient is transformed to a normal dependence with increasing friction coefficient $\gamma'$. It has been found that a temperature-abnormal diffusivity "window" arises at certain friction coefficients. The diffusion coefficient first increases with decreasing temperature in a certain force interval and, then, decreases again. The diagrams of existence of such regions have been plotted.