Roughness density

TL;DR

This paper introduces a new observable to measure the roughness of displacement fields in disordered elastic systems, including those with overhangs and defects, advancing the understanding of interface physics.

Contribution

It proposes a novel measure for roughness that accounts for non-smooth features, extending the analysis beyond traditional elastic descriptions.

Findings

The observable can quantify roughness beyond elastic limits.

It captures overhangs and defects in displacement fields.

Supports development of a general interface theory.

Abstract

The theory of disordered elastic systems is one of the most powerful frameworks to assess the physics of multiple systems that span from ferromagnets to migrating biological cells. In this formalism, one assumes that the system can be described with a displacement field. This field can represent an interface position, the deformation of a vortex lattice or charge density waves in semiconductor devices, among others. By construction, this field is univalued and 'smooth', and, even if experimental realisations of it can be far from this description, the consequences of these approximations have not been yet fully explored. We present a new observable to measure the roughness of displacement fields that can be beyond the elastic limit and can contain overhangs and other defects. Our observable represents a stepping stone towards the construction of a general theory for interfaces.