Memory-induced current reversal of Brownian motors

TL;DR

This work investigates how memory effects in a viscoelastic bath modify transport in Brownian motors, using a Generalized Langevin Equation with memory kernel $K(t)$. The authors study a rocking Brownian ratchet in an exponential memory bath and compare full non-Markovian dynamics to an effective-mass approximation with $m^* = m - \Delta m(\tau)$. They demonstrate a memory-induced current reversal as the memory time $\tau$ grows and show that it can be understood both by the reduced effective mass and by memory-driven dynamical localization into a negative-velocity attractor with period-averaged velocity $v(t)$. The results highlight memory as a controllable parameter for nanoscale transport and have implications for biological motors and synthetic ratchets operating in viscoelastic environments.

Abstract

Kinetics of biological motors such as kinesin or dynein is notably influenced by viscoelastic intracellular environment. The characteristic relaxation time of the cytosol is not separable from the colloidal timescale and therefore their dynamics is inherently non-Markovian. In this paper we consider a variant of a Brownian motor model, namely a Brownian ratchet immersed in a correlated thermal bath and analyze how memory influences its dynamics. In particular, we demonstrate the memory-induced current reversal effect and explain this phenomenon by applying the effective mass approximation as well as uncovering the memory-induced dynamical localization of the motor trajectories in the phase space. Our results reveal new aspects of the role of memory in microscopic systems out of thermal equilibrium.

Figures (4)

• Figure 1: The average velocity of the particle $\langle v \rangle$ as a function of the memory time $\tau$ for the original system (Eq. \ref{['eq:gle']}) as well as the effective mass approximation (Eq. \ref{['eq:eff_mass']}) in the first and second order. In the inset for $\tau = 0.04$ we show the same characteristic but versus the amplitude $a$ of the external driving force.
• Figure 2: The average velocity $\langle v \rangle$ of the particle versus the temperature $D$ for different memory times $\tau$ and the memoryless limit $\tau\to0$.
• Figure 3: The probability distribution $P(\mathsf{v}(t))$ for the period averaged velocity $\mathsf{v}(t)$ in the memoryless system $\tau \to 0$ for the long time limit calculated from histogram consisting of 150 and 3 bins.
• Figure 4: The probabilities $P_\pm$ and $P_0$ for the emergence of the states $\mathsf{v}_\pm = \pm \omega/(2\pi)$ and $\mathsf{v}_0 = 0$, respectively, versus the memory time $\tau$.