Abstract
Ratchets are devices able to rectify an otherwise oscillatory behavior by exploiting an asymmetry of the system. In rocking ratchets the asymmetry is induced through a proper choice of external forces and modulations of nonlinear symmetric potentials. The ratchet currents thus obtained in systems as different as semiconductors, Josephson junctions, optical lattices, or ferrofluids, show a set of universal features. A satisfactory explanation for them has challenged theorist for decades, and so far we still lack a general theory of this phenomenon. Here we provide such a theory by exploring ---through functional analysis--- the constraints that the simple assumption of time-shift invariance of the ratchet current imposes on its dependence on the external drivings. Because the derivation is based on so general a principle, the resulting expression is valid irrespective of the details and the nature of the physical systems to which it is applied, and of whether they are classical, quantum, or stochastic. The theory also explains deviations observed from universality under special conditions, and allows to make predictions of phenomena not yet observed in any experiment or simulation.
Highlights
Forcing nonlinear transport systems with zero-average, time-periodic, external forces may generate a ratchet current [1]
The ratchet currents obtained in systems as different as semiconductors, Josephson junctions, optical lattices, or ferrofluids show a set of universal features
We explore the constraints that the simple time-shift invariance satisfied by the ratchet current imposes on its shape and derive an expression that explains all observations described above, both for harmonic mixing and gating ratchets
Summary
Forcing nonlinear transport systems with zero-average, time-periodic, external forces may generate a ratchet current [1]. An alternative theoretical approach has been recently proposed for the case of harmonic mixing [38] This theory does capture the nonzero phase lag that the ratchet current normally exhibits and predicts a nonzero current for square-wave forces [41]. Despite this relative success, a general theory that encompasses a unified explanation of all universal features observed in so wide a diversity of systems, an explanation of the deviations from them that occur outside the small-amplitude regime and the effects induced by further harmonics, is still lacking. What the theory does predict is that the current must necessarily be zero if the system possesses some specific symmetries—so it is consistent with the wellknown fact that, unless some symmetries are broken, a ratchet current cannot be generated [9,11,27]
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