DEPARTMENT OF CHEMISTRY

Theoretical Methods for Studying Current Inversion in Brownian Ratchets

The seemingly random movement of particles in equilibrium is characterized by Brownian motion, with particles equally likely to move in all directions. To perform useful work, however, we frequently require directional transport. Think, for example, of electrons flowing one way through a wire or molecular motors marching along a filament. We might think of the electrons in the wire as flowing "downhill" from one electrode of a battery to another. Past theoretical and experimental studies from the Ratner and Weiss groups have illuminated an alternative way to generate directed flows even in the absence of such a downhill thermodynamic driving force. Rather, one applies a time-periodic perturbation to drive a ratcheting mechanism. Remarkably, even when that perturbation is symmetric (pushing a particle to the right as often as to the left), the particle's Brownian motion can collude with the driving to yield net directed motion, and that direction of that motion is not always simple to anticipate. In fact, the flow can switch direction just by changing the frequency of the perturbation, a so-called current reversal.

Researchers in Professor Todd Gingrich's group have developed theoretical tools to better understand this dynamical phenomena. Using their techniques, they have converted from studying trajectories undergoing driven Brownian motion into solving an associated eigenvalue problem, of the sort typically more familiar to quantum chemistry applications. That mapping enabled them to efficiently compute the impact of driving frequency on current and explain the origin of the current reversal. In addition to applications in developing and designing such ratchets, the numerical techniques should prove useful for analyzing other systems with noisy dynamics. Their work was recently featured as an Editor's Suggestion in Physical Review E (2020, 102, 012141).