Scaling properties in off equilibrium dynamical processes

Abstract

In the present paper, we analyze the consequences of scaling hypotheses on dynamic functions, as two times correlations $C(t,t^{\prime })$. We show, under general conditions, that $C(t,t^{\prime })$ must obey the following scaling behavior $C(t,t^{\prime })={\varphi }_1(t{)}^{f(\beta )}\mathcal{S}(\beta )$, where the scaling variable is $\beta =\beta ({\varphi }_1(t^{\prime })/{\varphi }_1(t))$ and ${\varphi }_1(t^{\prime })$, ${\varphi }_1(t)$ two undetermined functions. The presence of a non constant exponent $f(\beta )$ signals the appearance of multiscaling properties in the dynamics.

6 pages, no figures