Conclusive mathematical arguments are presented supporting the ratchet conjecture [R. Chac\'{ o}n, J. Phys. A \textbf{ 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 \textit{ unique} for both temporal and spatial biharmonic forces, and general (\textit{ 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 \textit{ any} application of the ratchet effect induced by symmetry breaking of temporal and spatial biharmonic forces.
Categories: nlin.CD physics.class-ph