Force-Force Correlator for Driven Disordered Systems at Finite Temperature

TL;DR

This paper investigates the fluctuations of pinning forces in driven disordered elastic systems at finite temperature and velocity, analyzing the crossover between depinning and equilibrium fixed points.

Contribution

It extends the understanding of force-force correlations to finite temperature and velocity, providing a numerical analysis of the crossover between known fixed points.

Findings

Identifies the behavior of force fluctuations across the entire parameter space.

Quantifies the crossover between depinning and equilibrium fixed points.

Provides numerical results for the force-force correlator at finite temperature and velocity.

Abstract

When driving a disordered elastic manifold through quenched disorder, the pinning forces exerted on the center of mass are fluctuating, with mean $f_c=-\overline{F_w} $ and variance $\Delta(w)=\overline{F_w F_0}^c$, where $w$ is the externally imposed control parameter for the preferred position of the center of mass. $\Delta(w)$ was obtained via the functional renormalization group in the limit of vanishing temperature $T\to 0$, and vanishing driving velocity $v\to 0$. There are two fixed points, and deformations thereof, which are well understood: The depinning fixed point ($T\to 0$ before $v\to 0$) rounded at $v>0$, and the zero-temperature equilibrium fixed point ($v\to 0$ before $T\to 0$) rounded at $T>0$. Here we consider the whole parameter space of driving velocity $v>0$ and temperature $T>0$, and quantify numerically the crossover between these two fixed points.