Criticality-induced universitality in ratchets

Abstract

Conclusive mathematical arguments are presented supporting the ratchet conjecture [R. Chacón,J. Phys. A 40, F413 (2007)], i.e., the existence of a universal force wave form 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.