The ratchet effect and the transporting islands in the chaotic sea

TL;DR

This paper investigates how directed transport occurs in a classical dissipative system with mixed phase space, revealing that stability islands in the chaotic sea can generate significant ratchet currents independent of initial conditions.

Contribution

It demonstrates that transporting stability islands in the Hamiltonian limit lead to large ratchet currents in dissipative systems with mixed phase space, a novel insight.

Findings

Large ratchet currents are generated by stability islands.

Stationary current values are independent of initial conditions.

Transporting islands exist within the chaotic sea in the Hamiltonian limit.

Abstract

We study directed transport in a classical deterministic dissipative system. We consider the generic case of mixed phase space and show that large ratchet currents can be generated thanks to the presence, in the Hamiltonian limit, of transporting stability islands embedded in the chaotic sea. Due to the simultaneous presence of chaos and dissipation the stationary value of the current is independent of initial conditions, except for initial states with very small measure.