Slow relaxation, anomalous diffusion, and aging in equilibrated or nonequilibrated environments
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Аннотация
In many complex systems such as glasses, polymers, proteins ..., temporal evolutions differ from standard laws, and are often much slower. Very slowly relaxing systems display aging effects. In particular, the time-scale of the response to an external perturbation, and/or of the associated correlation function, increases with the age of the system. In such situations, time-invariance properties are lost, and the fluctuation-dissipation theorem (FDT) does not hold.
Classically, the out of equilibrium violation of the FDT is characterized by a fluctuation-dissipation ratio, which is a function of both the observation time $\tau$ and the waiting time (or age) $t_w$. One may associate to this ratio an effective temperature, governing the slow dynamics, and sharing some properties of a temperature in the thermodynamic sense. These concepts are currently under experimental investigation in glassy systems and in granular materials.
A system well adapted to the analysis of these concepts is a diffusing particle in contact with an environment, which itself may be in equilibrium (thermal bath), or out of equilibrium (aging medium). Actually, a (possibly anomalously) diffusing particle is, first, an interesting system per se. Roughly speaking, its velocity thermalizes, but not its displacement with respect to a given initial position, which is out of equilibrium at any time. The violation of the corresponding FDT can be characterized by a fluctuation-dissipation ratio and an effective temperature. Besides, such a particle constitutes also a convenient tool for investigating the properties of its surrounding medium. In particular, in a non equilibrated aging environment, itself characterized by an effective temperature, a diffusing particle acts as a thermometer. Thus, independent measurements of the mean-square displacement and of the mobility of a micrometer bead immersed in an aging medium such as a colloidal glass give access to an out of equilibrium generalized Stokes-Einstein relation, from which the effective temperature of the medium can eventually be deduced.