Response Function of Coarsening Systems

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.