Driven particle dispersion in narrow disordered racetracks

We study the disorder-induced deterministic dispersion of particles uniformly driven in an array of narrow tracks. For different toy models with quenched disorder we obtain exact analytical expressions for the steadystate mean velocity v and the dispersion constant D for any driving force f above the depinning threshold. For short-range correlated pinning forces we find that at large drives D similar to 1/v for random-field type of disorder while D similar to 1/v3 for the random-bond type. We show numerically that these results are robust: the same scaling holds for models of massive damped particles, soft particles, particles in quasi-one-dimensional or two-dimensional tracks, and for a model of a magnetic domain wall with two degrees of freedom driven either by electrical current or magnetic field. Crossover and finite-temperature effects are discussed. The universal features we identify may be relevant for describing the fluctuating dynamics of stable localized objects such as solitons, superconducting vortices, magnetic domain walls and skyrmions, and colloids driven in quasi-one-dimensional track arrays. In particular, the drive dependence of D appears as a sensitive tool for characterizing and assessing the nature of disorder in the host materials.

Automated summary

We study the deterministic dispersion of particles uniformly driven in an array of narrow tracks induced by disorder. We obtain analytical expressions for the mean velocity and dispersion constant for different toy models with quenched disorder. We find that the relationship between the dispersion constant and velocity depends on the type of disorder. These results are robust across different models and effects, and may have implications for understanding the dynamics of stable localized objects in various systems.