Response Function of Coarsening Systems

TL;DR

This paper investigates the response functions in coarsening systems, analyzing how the fluctuation-dissipation ratio behaves over time and how the domain-wall response scales with domain size in different dimensions.

Contribution

It provides an analytical and numerical study of the pre-asymptotic domain-wall response and its scaling with domain size in coarsening systems.

Findings

The fluctuation-dissipation ratio tends to 1 or 0 depending on the correlation value.

The domain-wall response scales as 1/L(t) for d>2.

In d=2, the response scales as ln(L(t))/L(t).

Abstract

The response function of domain growth processes, and in particular the violation of the fluctuation-dissipation theorem, are studied both analytically and numerically. In the asymptotic limit of large times, the fluctuation-dissipation ratio $X$, which quantifies this violation, tends to one if $C>m^2$ and to zero if $C<m^2$, corresponding to the fast (`bulk') and slow (`domain-wall') responses, respectively. In this paper, we focus on the pre-asymptotic behavior of the domain-wall response. This response is shown to scale with the typical domain length $L(t)$ as $1/L(t)$ for dimension $d>2$, and as $\ln (L(t))/L(t)$ for $d=2$. Numerical results confirming this analysis are presented.