Beyond giant enhanced diffusion in tilted logarithmic periodic potentials

We investigate diffusion enhancement in tilted periodic potentials with distinct forms and symmetries. Using the first-passage time representation of the effective diffusion coefficient and Monte Carlo simulations, we compare four types of potentials: symmetric tilted sinusoidal periodic potential (TSPP), asymmetric TSPP, symmetric tilted logarithmic periodic potential (TLPP), and asymmetric TLPP. We find that symmetry breaking in sinusoidal potentials does not always lead to stronger diffusion enhancement, while the logarithmic form, due to its weak confinement, exhibits robust amplification. Importantly, the asymmetric TLPP combines weak confinement with pronounced wave-packet splitting, and therefore exhibits the strongest diffusion enhancement among the four cases considered. Our results indicate that, within the considered model and parameter regimes, the form of the periodic structure, beyond symmetry considerations, can significantly influence diffusion amplification, and may provide useful guidance for the design of potential landscapes in nonequilibrium statistical physics.