Motional dispersions and ratchet effect in inertial systems

We obtain ratchet effect in inertial structureless systems in symmetric periodic potentials where the asymmetry comes from the non-uniform 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 work.