Optimal driving waveform for overdamped, adiabatic rocking ratchets

TL;DR

This paper identifies the optimal dichotomous driving waveform for overdamped, adiabatic rocking ratchets to maximize particle velocity, with implications for nanotechnological transport device design.

Contribution

It demonstrates that the optimal waveform is dichotomous within a broad class of admissible functions, advancing the understanding of ratchet optimization.

Findings

Optimal waveform is dichotomous for maximum particle velocity.

Results applicable to a broad class of adiabatic responses.

Implications for designing efficient nanotechnological ratchets.

Abstract

As a first step in the project of ratchet optimisation, the optimal driving waveform among a wide class of admissible functions for an overdamped, adiabatic rocking ratchet is shown to be dichotomous. `Optimum' is defined as that which achieves the maximum (or minimum negative) average particle velocity. Implications for the design of ratchets, for example in nanotechnological transport, may follow. The main result is applicable to a general class of adiabatic responses.