Occurrence and robustness of current reversals in overdamped deterministic ratchets under symmetric forcing

Abstract

We analyze the conditions for the existence of current reversals in overdamped deterministic tilting ratchets under symmetric forcing. To this end, we use and extend the formalism recently introduced in R. Salgado-García, M. Aldana, and G. Martinez-Mekler [Phys. Rev. Lett. 96, 134101 (2006)] to transform the equations of motion of the ratchet into discrete circle maps. For a periodic dichotomous forcing we show that the phenomenon of current reversal is not uncommon and exists for a nonzero measure set of the parameter space. Additionally, we show numerically that, for a wide class of ratchet potentials, current reversals also occur when the discontinuous dichotomous forcing is replaced by symmetric continuous driving forces. The likelihood of the occurrence of current reversals is a consequence of the structural stability under small perturbations of the associated circle map with rational rotation number.