Equilibrium and off-equilibrium dynamics in a model for vortices in superconductors

We study a model for the dynamics of vortices in type-II superconductors. In particular, we discuss the magnetization relaxation close to and off equilibrium. At low temperatures a crossover point is found, $T_g,$ where relaxation times become huge and seem to diverge according a Vogel-Tamman-Fulcher law at a lower temperature $T_c$ where a thermodynamic glass transition might be located. Magnetic creep changes by crossing $T_g:$ below $T_g,$ vortex motion is strongly subdiffusive and logarithmic creep is found; above $T_g,$ a power-law creep is asymptotically followed by stretched exponential saturation. The analysis of the self-scattering function also reveals that the dynamical process is non-Gaussian. In the regime below $T_g,$ strong “memory” and “aging” effects appear. In particular, we analyze the properties of “aging” and the structure of its “dynamical scaling.”