Criticality-induced universality in ratchets
Abstract
Conclusive mathematical arguments are presented supporting the ratchet conjecture [R. Chac\'on, J. Phys. A 40, F413 (2007)], i.e., the existence of a universal force waveform which optimally enhances directed transport by symmetry breaking. Specifically, such a particular waveform is shown to be unique for both temporal and spatial biharmonic forces, and general (non-perturbative) laws providing the dependence of the strength of directed transport on the force parameters are deduced for these forces. The theory explains previous results for a great diversity of systems subjected to such biharmonic forces and provides a universal quantitative criterion to optimize any application of the ratchet effect induced by symmetry breaking of temporal and spatial biharmonic forces.
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