We obtain ratchet effect in inertial structureless systems in symmetric periodic potentials where the asymmetry comes from the nonuniform friction offered by the medium and driven by symmetric periodic forces. In the adiabatic limit the calculations are done by extending the matrix continued fraction method and also by numerically solving the appropriate Langevin equation. For finite frequency field drive the ratchet effect is obtained only numerically. In the transient time scales the system shows dispersionless behaviour as reported earlier when a constant force is applied. In the periodic drive case the dispersion behaviour is more complex. In this brief communication we report some of the results of our workComment: 14 pages, 7figure

We numerically solve the underdamped Langevin equation to obtain the trajectories of a particle in a sinusoidal potential driven by a temporally sinusoidal force in a medium with coefficient of friction periodic in space as the potential but with a phase difference. With the appropriate choice of system parameters, like the mean friction coefficient and the period of the applied field, only two kinds of periodic trajectories are obtained for all possible initial conditions at low noise strengths: one with a large amplitude and a large phase lag with respect to the applied field and the other with a small amplitude and a small phase lag. Thus, the periodic potential system is effectively mapped dynamically into a bistable system. Though the directional asymmetry, brought about only by the frictional inhomogeneity, is weak we find both the phenomena of stochastic resonance, with ready explanation in terms of the two dynamical states of trajectories, and ratchet effect simultaneously in the same parameter space. We analyse the results in detail attempting to find plausible explanations for each.

We extend Risken's matrix continued fraction method (MCFM) to solve the Fokker-Planck equation to calculate the particle current in an inertial symmetric (sinusoidal) periodic potential under the action of a constant force. We consider particle motion in a medium with a small friction coefficient varying periodically in space as the potential but with a finite phase difference φ( = nπ, n = 0, 1, 2, . . .). Though the frictional inhomogeneity is considered a less likely candidate to trigger the ratchet effect than the temperature inhomogeneity, for the former leaves the static equilibrium distribution unaffected as opposed to the latter, it results in a finite net algebraic sum of currents with symmetrically time-distributed small applied forces ±|F |. The MCFM results, with very rich and interesting qualitative characteristics, are supported by Langevin dynamic simulations. The effects of different uniform F , temperature T and average friction coefficient γ 0 on the performance characteristics of the inhomogeneous ratchet are presented.

We have studied the motion of an underdamped Brownian particle in (i) a bistable periodic potential and (ii) washboard potentials subjected to a sinusoidal external field. The particles are shown to be effectively in two dynamical states of their trajectories with distinct amplitudes and phase relationship with the external drive. These dynamical states are stable with fixed energies at low temperatures, but transitions between them take place as the temperature is increased. The average input energy loss to the environment per period of the drive shows a stochastic resonance (SR) peak as a function of temperature for the underdamped system potentials studied. The occurrence of SR in these systems is explained using the statistics of transitions between the two dynamical states.

Recently, stochastic resonance was shown to occur in underdamped periodic potentials at frequencies (of the drive field) close to the natural frequency at the minima of the potentials. In these systems the particle trajectories are not arbitrary at low temperatures but follow the drive field with two definite mean phase differences depending on the initial conditions. The trajectories are thus found to be in only two stable dynamical states. The occurrence of stochastic resonance in the periodic potentials was explained as a consequence of the transitions between these two dynamical states as the temperature was increased. In the present work, we find the range of amplitudes of the drive field over which the dynamical states could be observed in a sinusoidal potential. The variation of the relative stability of the dynamical states as a function of drive-field amplitude is clarified by analyzing the nature of curves characterizing the stochastic resonance as the amplitude is varied within the range.