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Center for Nonlinear Studies |
Ratchet or rectification phenomena appear in many different fields ranging from nanodevices to molecular biology. In the simplest model a point-like particle is considered which is driven by deterministic or non-white stochastic forces. Under certain conditions related to the breaking of symmetries, unidirectional motion of the particle can take place although the applied force has zero average in time. These particle ratchets have recently been generalized to spatially extended nonlinear systems, in which solitons play a similar role as the above point particles. E.g., solitons in nonlinear Klein-Gordon systems have been shown to move on the average in one direction, although the driving force has zero time average, if either a temporal or a spatial symmetry is broken. In the first case, we have used a biharmonic driving force which produces a pronounced ratchet effect. The effect has been confirmed by experiments with Josephson junctions, where fluxons play the role of the solitons, and by experiments on optical lattices. This shows that such soliton ratchet models are generic because they apply to experiments in quite different fields. In the second case, we have introduced point-like inhomogeneities which break the spatial symmetry and yield a ratchet effect with the following features: The average soliton velocity either increases with the driving amplitude like a staircase or it is non-zero only for certain ranges of the driving amplitude (so-called windows). We have tried to optimize the above soliton ratchet systems, which obviously is important for the design of experiments and technical devices. This can be achieved in various ways: E.g., the structure of the periodic array of inhomogeneities and the shape of the inhomogeneities can be optimized. Moreover, we have shown that the ratchet effect is robust under the influence of thermal noise. It's even possible that for certain parameter ranges the effect is maximal for a certain temperature. Or, for a given temperature there is an optimal set of parameters, which is important for biological and technical applications.