Weak-Chaos Ratchet Accelerator

TL;DR

This paper introduces a Hamiltonian ratchet accelerator that produces directed momentum current even under weak chaos, with analytical solutions showing maximal current in the weak chaos limit.

Contribution

It presents a new Hamiltonian model, a generalized kicked rotor, capable of generating momentum current at arbitrarily weak chaos, unlike previous models requiring strong chaos.

Findings

Momentum current exists for arbitrarily weak chaos.

Analytical expressions for the current are derived.

Maximum current occurs in the weak chaos limit.

Abstract

Classical Hamiltonian systems with a mixed phase space and some asymmetry may exhibit chaotic ratchet effects. The most significant such effect is a directed momentum current or acceleration. In known model systems, this effect may arise only for sufficiently strong chaos. In this paper, a Hamiltonian ratchet accelerator is introduced, featuring a momentum current for arbitrarily weak chaos. The system is a realistic, generalized kicked rotor and is exactly solvable to some extent, leading to analytical expressions for the momentum current. While this current arises also for relatively strong chaos, the maximal current is shown to occur, at least in one case, precisely in a limit of arbitrarily weak chaos.