  We discuss aging and localization in a simple "Eshelby" mesoscopic model of
amorphous plasticity. Plastic deformation is assumed to occur through a series
of local reorganizations. Using a discretization of the mechanical fields on a
discrete lattice, local reorganizations are modeled as local slip events. Local
yield stresses are randomly distributed in space and invariant in time. Each
plastic slip event induces a long-ranged elastic stress redistribution.
Mimicking the effect of aging, we focus on the behavior of the model when the
initial state is characterized by a distribution of high local yield stress
values. A dramatic effect on the localization behavior is obtained: the system
first spontaneously self-traps to form a shear band which then only slowly
widens. The higher the "age" parameter the more localized the plastic strain
field. Two-time correlation computed on the stress field show a divergent
correlation time with the age parameter. The amplitude of a local slip event
(the prefactor of the Eshelby singularity) as compared to the yield stress
distribution width acts here as an effective temperature-like parameter: the
lower the slip increment, the higher the localization and the decorrelation
time.
