Memory-Induced Transport and Arrest in Flashing Ratchets: From Superdiffusion to Clustering

TL;DR

The study addresses how memory effects from colored noise interact with a flashing ratchet and interparticle interactions to shape transport in one dimension. It uses a generalized Langevin framework with a bi-exponential memory kernel driving a flashing sawtooth potential, analyzed for both non-interacting and single-file hard-core particles. For non-interacting particles, the two-frequency memory kernel enhances transport and yields superdiffusive $MSD$ behavior with a slope near 2, while in single-file systems the same noise triggers clustering at ratchet minima, causing current arrest and $MSD$ saturation; importantly, this clustering exhibits universal scaling across densities with a crossover time $t_c \propto 1/\rho$ and no finite critical density. These findings reveal robust, counterintuitive effects of non-Markovian noise in confined systems, with potential implications for transport in crowded or confined environments such as colloidal suspensions, molecular motors, and microfluidic ratchet devices.

Abstract

We investigate the transport properties of particles driven by colored noise in a flashing ratchet potential, focusing on both non-interacting and single-file interacting regimes. The model incorporates memory effects via a non-Markovian friction kernel, leading to superdiffusive dynamics and enhanced currents in the absence of interactions. However, when particles are constrained to single-file motion with hard-core repulsion, the same non-Markovian noise induces a dynamical transition: initial superdiffusion gives way to the formation of static clusters, ultimately suppressing net current. This transition occurs without a critical density and results from the interplay between noise persistence and the ratchet's potential. Our numerical results reveal a universal scaling behavior for the mean square displacement across densities, suggesting robustness of the clustering mechanism. These findings have potential implications for transport in crowded or confined systems such as colloidal suspensions, molecular motors in cellular environments, or microfluidic devices, where controlling noise and crowding can be used to tune transport efficiency.

Figures (5)

• Figure 1: Comparison of (a) current $J$ and (b) mean-squared displacement ($MSD$) as functions of time for non-interacting particles subjected to colored noise with two characteristic frequencies (red line) and with a single characteristic frequency (green and blue lines). In all cases, the particle density is fixed at $\rho = 1$. The two-frequency noise yields higher transport efficiency. The dashed line in panel (b) has slope 1.9 and is shown as a reference. (Representative error bars are shown in panel (a)).
• Figure 2: Comparison of (a) $J$ and (b) the $MSD$ vs. time for interacting particles under colored noise with two characteristic frequencies (red line) and with one characteristic frequency (green and blue lines). The particle density $\rho = 0.06$ for all cases. In the first case, particle interactions suppress $J$, resulting in a plateau of the $MSD$. (Representative error bars are shown in panel (a).
• Figure 3: Schematic illustration of cluster formation in a single-file system of particles subjected to colored noise with two characteristic frequencies.
• Figure 4: MSD and $\langle |(x-x_0)|\rangle$ versus time for $U_0 = 0$ and colored noise with two characteristic frequencies on a log–log scale, for a single-file system (red line) and free particles (blue line). The particle density $\rho = 0.06$ for both cases. The behavior with time predicted by Eq. (\ref{['single-file']}) is satisfied in the steady state.
• Figure 5: (a) $MSD$ versus time for $t_p/2 = 0.3$, $\alpha = 0.9$, and different particle densities $\rho$ under two-frequency colored noise. (b) Scaled $MSD$ as a function of $t\rho$. Inset: $\rho$ vs. $1/t_c$ with linear fit (red line).