Scaling properties in off equilibrium dynamical processes

TL;DR

This paper investigates the scaling behavior of two-time correlation functions in off-equilibrium dynamical processes, revealing conditions under which multiscaling properties emerge due to variable exponents.

Contribution

It introduces a general scaling form for correlation functions in off-equilibrium dynamics, highlighting the role of variable exponents in multiscaling phenomena.

Findings

Correlation functions follow a specific scaling form involving functions of time.

Presence of a non-constant exponent indicates multiscaling behavior.

Provides a theoretical framework for understanding off-equilibrium dynamics.

Abstract

In the present paper, we analyze the consequences of scaling hypotheses on dynamic functions, as two times correlations $C(t,t')$. We show, under general conditions, that $C(t,t')$ must obey the following scaling behavior $C(t,t') = \phi_1(t)^{f(\beta)}{\cal{S}}(\beta)$, where the scaling variable is $\beta=\beta(\phi_1(t')/\phi_1(t))$ and $\phi_1(t')$, $\phi_1(t)$ two undetermined functions. The presence of a non constant exponent $f(\beta)$ signals the appearance of multiscaling properties in the dynamics.