Criticality-induced universality in ratchets

TL;DR

This paper provides mathematical proof supporting the existence of a universal force waveform that optimally enhances directed transport in ratchet systems, explaining previous results and offering a universal criterion for optimization.

Contribution

It establishes the uniqueness of the optimal force waveform for biharmonic forces and derives general laws relating force parameters to directed transport strength.

Findings

Proves the existence of a universal optimal force waveform for ratchets.

Shows the uniqueness of this waveform for biharmonic forces.

Provides laws linking force parameters to transport efficiency.

Abstract

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.