Collective Transport: From Superconductors to Earthquakes

TL;DR

This paper explores non-equilibrium transport phenomena involving elastic manifolds driven through random media, focusing on depinning transitions and their applications to systems like superconductors, earthquakes, and crack dynamics.

Contribution

It introduces a unified scaling framework for depinning phenomena and applies it to diverse physical systems, connecting theoretical models with real-world applications.

Findings

Mean field theory captures key depinning behaviors

Avalanche models explain sudden system responses

Scaling laws unify different physical systems

Abstract

In these lectures, a variety of non-equilibrium transport phenomena are introduced that all involve, in some way, elastic manifolds being driven through random media. A simple class of models is studied focussing on the behavior near to the critical ``depinning'' force above which persistent motion occurs in these systems. A simple mean field theory and a ``toy'' model of ``avalanche'' processes are analyzed and used to motivate the general scaling picture found in recent renormalization group studies. The general ideas and results are then applied to various systems: sliding charge density waves, critical current behavior of vortices in superconductors, dynamics of cracks, and simple models of a geological fault. The roles of thermal fluctuations, defects, inertia, and elastic wave propagation are all discussed briefly.