Deterministic ratchets: route to diffusive transport

TL;DR

This paper investigates how the efficiency of underdamped ratchets in the adiabatic regime depends on damping, revealing a transition from regular to chaotic transport that affects rectification performance.

Contribution

It provides a numerical study of the transition from regular to chaotic transport in noiseless ratchets and characterizes the conditions affecting rectification efficiency.

Findings

Rectification efficiency scales with current amplitude near a critical damping threshold.

Below the threshold, the rectified signal becomes irregular and averages to zero.

Periodic and chaotic trajectories coexist, influencing transport behavior.

Abstract

The rectification efficiency of an underdamped ratchet operated in the adiabatic regime increases according to a scaling current-amplitude curve as the damping constant approaches a critical threshold; below threshold the rectified signal becomes extremely irregular and eventually its time average drops to zero. Periodic (locked) and diffusive (fully chaotic) trajectories coexist on fine tuning the amplitude of the input signal. The transition from regular to chaotic transport in noiseless ratchets is studied numerically.