The Large Scale Energy Landscapes of Randomly Pinned Objects

TL;DR

This paper analyzes the large-scale energy landscape of elastic manifolds in random pinning potentials using FRG and replica methods, revealing a hierarchical structure of parabolic wells affecting their dynamics.

Contribution

It introduces a hierarchical model of the energy landscape for pinned elastic objects, combining FRG and replica approaches to understand their large-scale behavior.

Findings

Energy landscape consists of parabolic wells of random depth.

Hierarchical subdivision of parabolas reflects smaller scale motions.

Implications for the dynamics of pinned elastic objects.

Abstract

We discuss the large scale effective potential for elastic objects (manifolds) in the presence of a random pinning potential, from the point of view of the Functional Renormalisation Group (FRG) and of the replica method. Both approaches suggest that the energy landscape at large scales is a succession of parabolic wells of random depth, matching on singular points where the effective force is discontinuous. These parabolas are themselves subdivided into smaller parabolas, corresponding to the motion of smaller length scales, in a hierarchical manner. Consequences for the dynamics of these pinned objects are underlined.