Dynamical States, Stochastic Resonance and Ratchet Effect in a Biharmonically Driven Sinusoidal Potential

TL;DR

This paper investigates how a biharmonically driven sinusoidal potential exhibits stable dynamical states, enabling the simultaneous occurrence of stochastic resonance and ratchet effects, with the phenomena depending on system parameters and temperature.

Contribution

It demonstrates the coexistence of stochastic resonance and ratchet effects in a driven sinusoidal system, highlighting the role of dynamical states and parameter choices.

Findings

Stable dynamical states exist at low temperatures.

Biharmonic drive enables ratchet effect over large parameter space.

Stochastic resonance occurs in a restricted parameter domain.

Abstract

Two stable dynamical states of trajectories of an underdamped particle, under appropriate conditions, appear naturally in a sinusoidal potential when driven by a low amplitude biharmonic external field. These states are quite stable at low temperatures but make transitions between them as the temperature is raised. The proper choice of the biharmonic drive makes it possible for the system to show, at the same time, {\it{both}} the phenomena of stochastic resonance and ratchet effect. Ratchet effect, in this case, a consequence of the biharmonic drive, is obtained over a large domain of parameter space. However, stochastic resonance can be obtained only over a restricted (sub)domain of parameter space and owes its existence largely to the existence of the two dynamical states.