Ratchet effect on a relativistic particle driven by external forces

TL;DR

This paper analyzes how damping influences the ratchet effect in a relativistic particle driven by asymmetric forces, revealing that damping can induce and optimize ratchet currents even under symmetric driving conditions.

Contribution

It provides an explicit solution for the ratchet velocity as a non-linear functional of the external force and demonstrates the counterintuitive role of damping in generating ratchet effects.

Findings

Damping can induce a ratchet current in symmetric, time-reversible systems.

The ratchet velocity can be expressed via a functional Taylor expansion.

Maximum ratchet current occurs at an optimal damping level.

Abstract

We study the ratchet effect of a damped relativistic particle driven by both asymmetric temporal bi-harmonic and time-periodic piecewise constant forces. This system can be formally solved for any external force, providing the ratchet velocity as a non-linear functional of the driving force. This allows us to explicitly illustrate the functional Taylor expansion formalism recently proposed for this kind of systems. The Taylor expansion reveals particularly useful to obtain the shape of the current when the force is periodic, piecewise constant. We also illustrate the somewhat counterintuitive effect that introducing damping may induce a ratchet effect. When the force is symmetric under time-reversal and the system is undamped, under symmetry principles no ratchet effect is possible. In this situation increasing damping generates a ratchet current which, upon increasing the damping coefficient eventually reaches a maximum and decreases toward zero. We argue that this effect is not specific of this example and should appear in any ratchet system with tunable damping driven by a time-reversible external force.