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Deterministic Ratchets, Circle Maps, and Current Reversals R. Salgado-Garcia,1,2

Summary: Deterministic Ratchets, Circle Maps, and Current Reversals
R. Salgado-Garci´a,1,2
M. Aldana,2
and G. Marti´nez-Mekler2
Facultad de Ciencias, UAEM, Avenida Universidad 1001 Colonia Chamilpa, 62210 Cuernavaca, Morelos, Mexico
Centro de Ciencias Fi´sicas, UNAM, C.P. 62251. Apartado Postal 48-3, Cuernavaca, Morelos, Mexico
(Received 18 October 2005; published 3 April 2006)
In this work we transform the deterministic dynamics of an overdamped tilting ratchet into a discrete
dynamical map by looking stroboscopically at the continuous motion originally ruled by differential
equations. We show that, for the simple and widely used case of periodic dichotomous driving forces, the
resulting discrete map belongs to the class of circle homeomorphisms. This approach allows us to apply
the well-known properties of such maps to derive the necessary and sufficient conditions that the ratchet
potential must satisfy in order to have a vanishing current. Furthermore, as a consequence of the above, we
show (i) that there is a class of periodic potentials which do not exhibit the rectification phenomenon in
spite of their asymmetry and (ii) that current reversals occur in the deterministic case for a large class of
ratchet potentials.
DOI: 10.1103/PhysRevLett.96.134101 PACS numbers: 05.60.Cd, 05.45.ÿa
Ratchet models have recently been studied in several


Source: Aldana, Maximino - Centro de Ciencias Físicas, Universidad Nacional Autónoma de México


Collections: Physics