Resonant Activation in Asymmetric Potentials

TL;DR

This paper investigates how asymmetry in a potential affects the resonant activation phenomenon, revealing new behaviors in mean first passage times, current reversal, and noise dependence through numerical Langevin equation solutions.

Contribution

It introduces the impact of potential asymmetry on resonant activation, including current reversal and noise effects, supported by numerical analysis and comparison with existing models.

Findings

Potential asymmetry significantly influences RA effect.

Current reversal depends on switching frequency and asymmetry.

Resonant mean first passage times exhibit unexpected noise-dependent behavior.

Abstract

The resonant activation effect (RA) has been well studied in different ways during the last two decades. It consists in the presence of a minimum in the mean time spent by a Brownian particle to exit from a potential well in the presence of a fluctuating external force, as a function of the mean frequency (or the correlation time) of the latter. This work studies the role played by the asymmetry of a piecewise linear potential in the RA effect, and, in general, the behavior of the mean first passage time and the mean velocity of the particle crossing through the potential barrier. A strong dependence on the asymmetry of the potential has been found which can be put in relationship with the current in the ratchet whose the potential here used is an elementary module. In this case a current reversal as a function of the frequency of the switching potential occurs. Comparison of the calculations with the Doering-Gadua model have been performed, as well as comparison with smooth symmetrical potentials, by checking for the robustness of the resonant correlation time. The calculations have been done by solving numerically the Langevin equation in the presence of an uncorrelated Gaussian noise. The resonant mean first passage times show an unexpected behavior as a function of the thermal noise intensity. The related curves present for the different symmetries an unexpected inversion of their relative behavior beyond a certain threshold value of the noise. This means that the current reversal can only occur for weak noise intensities, lower than that threshold value.