Transient dynamics in the thermal ratchets transport model

TL;DR

This paper investigates the transient and asymptotic behaviors of a one-dimensional thermal ratchet model with periodic potential switching, revealing how system properties influence transport dynamics and convergence to steady state.

Contribution

It provides a numerical analysis of the full dynamics of the thermal ratchet model, highlighting transient behaviors and their dependence on system parameters.

Findings

Transient aperiodic behavior converges to periodic steady state.

Transport rate and transient lifetime depend on system properties.

Transient dynamics significantly influence overall transport performance.

Abstract

The thermal ratchets model toggles a spatially periodic asymmetric potential to rectify random walks and achieve transport of diffusing particles. We numerically solve the governing equation for the full dynamics of an infinite 1D ratchet model in response to periodic switching. Transient aperiodic behavior is observed that converges asymptotically to the period of the switching. We study measures of the transport rate, the transient lifetime, and an equivalent of `amplitude', then investigate their dependence on various properties of the system, along with other features of the transient and asymptotic dynamics.