Mean Field Theory of Collective Transport with Phase Slips

TL;DR

This paper develops a mean field theory for collective transport in disordered systems with phase slips, revealing complex phase diagrams, coexistence of phases, and hysteresis effects in driven plastic systems.

Contribution

It introduces a mean field framework that models phase slips in disordered systems, providing analytical and numerical insights into phase transitions and coexistence.

Findings

Phase diagrams show generic phases and boundaries influenced by disorder potential shape.

Coexistence of coherent and incoherent static phases is demonstrated.

Hysteretic transitions between moving and static phases are identified.

Abstract

The driven transport of plastic systems in various disordered backgrounds is studied within mean field theory. Plasticity is modeled using non-convex interparticle potentials that allow for phase slips. This theory most naturally describes sliding charge density waves; other applications include flow of colloidal particles or driven magnetic flux vortices in disordered backgrounds. The phase diagrams exhibit generic phases and phase boundaries, though the shapes of the phase boundaries depend on the shape of the disorder potential. The phases are distinguished by their velocity and coherence: the moving phase generically has finite coherence, while pinned states can be coherent or incoherent. The coherent and incoherent static phases can coexist in parameter space, in contrast with previous results for exactly sinusoidal pinning potentials. Transitions between the moving and static states can also be hysteretic. The depinning transition from the static to sliding states can be determined analytically, while the repinning transition from the moving to the pinned phases is computed by direct simulation.