Physica D 168–169 (2002) 205–219 Current reversals in deterministic ratchets: points and dimers José L. Mateos ∗ Instituto de F´ ısica, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Mexico, DF, Mexico Abstract We address the problem of the chaotic transport of point particles and rigid dimers in an asymmetric periodic ratchet potential. When the inertial term is taken into account, the dynamics can be chaotic and modify the transport properties. By a comparison between the bifurcation diagram and the current, we identify the origin of the multiple current reversals as bifurcations, usually from a chaotic to a periodic regime. We consider the dynamics of rigid dimers, as a function of size, extending in this way our previous results for point particles. © 2002 Elsevier Science B.V. All rights reserved. PACS: 05.45.Ac; 05.40.Fb; 05.45.Pq; 05.60.Cd Keywords: Deterministic ratchets; Chaotic transport; Current reversals 1. Introduction There is an increasing interest in recent years in the study of the transport properties of nonlinear systems that can extract usable work from unbiased non-equilibrium fluctuations. These so-called ratchet systems can be modeled, for instance, by considering a Brownian particle in a periodic asymmetric potential and acted upon by an external time-dependent force of zero average. This recent burst of work is motivated in part by the challenge to explain the unidirectional transport of molecular motors in the biological realm and the possibility for new methods of separation of particles. For recent reviews, see [1–4]. Although the vast majority of the literature in this field considers the presence of noise, very recently there has been motivations to understand in detail the transport properties of classical deterministic iner- tial ratchets [5–21]. These ratchets have in general a ∗ Tel.: +52-5-622-5130; fax: +52-5-622-5015. E-mail address: mateos@fisica.unam.mx (J.L. Mateos). classical chaotic dynamics that determines the trans- port properties. The implications of this chaotic dy- namics in deterministic ratchets have recently been address in the quantum domain, together with the possible connection with quantum chaos [22–24]. In particular, in a recent paper [6] we established, for the first time, a connection between the current generated in a deterministic rocking ratchet and the bifurcation diagram associated with chaotic dynam- ics. It turns out that when we plot the current, defined as an average velocity, against a control parameter of the system, we found multiple current reversals; on the other hand, we can obtain a bifurcation diagram plotting the velocity of the particle as a function of the same control parameter. We notice a clear con- nection between these two plots and by doing a close comparison we found that the current reversals occur associated with bifurcations. In many cases, these re- versals occur in crisis bifurcations from a chaotic to a periodic regime. It is worth mentioning that this prediction has been verified qualitatively in a recent experiment done by 0167-2789/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII:S0167-2789(02)00510-9