Dynamical states, stochastic resonance, and ratchet effect in a biharmonically driven sinusoidal potential

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, 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.

Particle dynamics in a symmetrically driven underdamped inhomogeneous periodic potential system

“…These are some of the questions that will be attempted to be clarified in a model system. These questions together have already been discussed earlier, however, in a uniform friction medium and subjected to a biharmonic external field [26], F (t) = F 0 (A cos(ωt) + B cos(2ωt)). In the present work, the potential is considered sinusoidal V (x) = −V 0 sin(x) and an external field of F (t) = F 0 cos(ωt).…”

“…From these figures one can observe that stochastic resonance and ratchet effect do occur simultaneously in the same parameter space. Note, however, that the temperatures at which < W > and homogeneous system was driven by a biharmonic forcing [26]. Figs.…”

Inertial frictional ratchets and their load bearing efficiencies

“…For example, a 'square-wave' drive with a large constant force for a small duration and a small constant force in the opposite direction for a longer duration [24] gives an appropriate asymmetric drive. A biharmonic drive being an another example [25,26] of asymmetric drive used to obtain ratchet current in overdamped as well as underdamped symmetric periodic potential systems. In most of the cases, in order to obtain ratchet current the medium (substrate) is considered spatially uniform so that the friction coefficient is constant in space.…”

“…Ratchet effect has been obtained in symmetrically periodic overdamped [33][34][35][36] as well as underdamped [11,24,26,[37][38][39] frictionally nonuniform systems. In Ref.…”

“…In the present work, for reason to be made clear later, we use larger frequency of period drive as in Ref. [26,38]. We consider the motion of underdamped particles in a sinusoidal potential V (x) = − sin x and driven by a sinusoidal external field F (t) = F 0 cos ωt with F 0 << F c , where F c is the critical field amplitude at which the barrier of the combined effective potential…”