Optimization of soliton ratchets in inhomogeneous sine-Gordon systems

TL;DR

This paper investigates how to optimize the design of inhomogeneities in sine-Gordon systems to maximize soliton ratchet velocity, combining theoretical analysis with numerical simulations.

Contribution

It introduces a collective coordinate approach to identify optimal inhomogeneity configurations for soliton ratchets in inhomogeneous sine-Gordon systems.

Findings

Optimal inhomogeneity arrangements produce double-peaked effective potentials.

Theoretical predictions are confirmed by numerical simulations.

Designing inhomogeneities with specific features enhances unidirectional soliton motion.

Abstract

Unidirectional motion of solitons can take place, although the applied force has zero average in time, when the spatial symmetry is broken by introducing a potential $V(x)$, which consists of periodically repeated cells with each cell containing an asymmetric array of strongly localized inhomogeneities at positions $x_{i}$. A collective coordinate approach shows that the positions, heights and widths of the inhomogeneities (in that order) are the crucial parameters so as to obtain an optimal effective potential $U_{opt}$ that yields a maximal average soliton velocity. $U_{opt}$ essentially exhibits two features: double peaks consisting of a positive and a negative peak, and long flat regions between the double peaks. Such a potential can be obtained by choosing inhomogeneities with opposite signs (e.g., microresistors and microshorts in the case of long Josephson junctions) that are positioned close to each other, while the distance between each peak pair is rather large. These results of the collective variables theory are confirmed by full simulations for the inhomogeneous sine-Gordon system.