Soliton ratchets out of point-like inhomogeneities

TL;DR

This paper presents a new design for a soliton ratchet using point-like inhomogeneities, combining theoretical predictions with numerical simulations, and highlights its potential applications in Josephson junctions and biological systems.

Contribution

The paper introduces a novel inhomogeneity-based ratchet mechanism for solitons, supported by a collective coordinate theory and numerical validation.

Findings

Effective asymmetric periodic potential induces ratchet effect.

Numerical simulations confirm theoretical predictions.

Applicable to Josephson junctions and biological systems.

Abstract

We introduce and study a novel design for a ratchet potential for soliton excitations. The potential is implemented by means of an array of point-like (delta) inhomogeneities in an otherwise homogeneous potential. We develop a collective coordinate theory that predicts that the effective potential acting on the soliton is periodic but asymmetric and gives rise to the ratchet effect. Numerical simulations fully confirm this prediction; quantitative agreement is reached by an improved version of the theory. Although we specifically show that it is most interesting for building Josephson junction ratchets capable to rectify time-symmetric ac forces, the proposed mechanism is very general and can appear in many contexts, including biological systems.