Soliton ratchets in homogeneous nonlinear Klein-Gordon systems

TL;DR

This paper investigates how bi-harmonic forces induce directed motion in topological solitons within nonlinear Klein-Gordon systems, highlighting the roles of symmetry breaking, resonance, and dissipation, supported by analytical and numerical methods.

Contribution

It introduces a collective coordinate approach revealing the mechanisms of soliton ratchet motion and analyzes the effects of dissipation and phase differences, supported by numerical simulations.

Findings

Directed soliton motion results from inhomogeneous energy pumping.

Breaking time-reversal symmetry is necessary for ratchet effects.

Dissipation and phase differences significantly influence velocity and current reversal.

Abstract

We study in detail the ratchet-like dynamics of topological solitons in homogeneous nonlinear Klein-Gordon systems driven by a bi-harmonic force. By using a collective coordinate approach with two degrees of freedom, namely the center of the soliton, $X(t)$, and its width, $l(t)$, we show, first, that energy is inhomogeneously pumped into the system, generating as result a directed motion; and, second, that the breaking of the time shift symmetry gives rise to a resonance mechanism that takes place whenever the width $l(t)$ oscillates with at least one frequency of the external ac force. In addition, we show that for the appearance of soliton ratchets, it is also necesary to break the time-reversal symmetry. We analyze in detail the effects of dissipation in the system, calculating the average velocity of the soliton as a function of the ac force and the damping. We find current reversal phenomena depending on the parameter choice and discuss the important role played by the phases of the ac force. Our analytical calculations are confirmed by numerical simulations of the full partial differential equations of the sine-Gordon and $\phi^4$ systems, which are seen to exhibit the same qualitative behavior. Our results are in agreement with recent experimental work on dissipation induced symmetry breaking.