Fluctuation-dissipation relation in a colloidal glass : frequency and aging time dependence
Résumé
We present an experimental and theoretical investigation of the Generalized Einstein Relation, a particular form of a fluctuation-dissipation relation, in an out-of-equilibrium complex fluid. Micrometer beads, used as thermometers, are immersed in an aging colloidal glass to provide both fluctuation and dissipation measurements. The fluctuation-dissipation ratio -- also expressed in terms of an effective temperature -- is derived as a function of frequency and aging time. We interpret the observed deviations from the Generalized Einstein Relation as directly related to the evolution of relaxation times of the glass with aging time. In accordance with our previous results, deviations are only observed in the regime where the observation time scale $1/\omega$ is of the order of a characteristic relaxation time $\tau$ of the glass, $\omega \tau \sim 1$. Our scenario is confirmed by measurements of the fluctuation-dissipation ratio in a wide range of frequencies, at long aging times.