Langevin simulations of the out-of-equilibrium dynamics of the vortex   glass in high-temperature superconductors
  We study the relaxation dynamics of flux lines in dirty high-temperature superconductors using numerical simulations of a London-Langevin model of the interacting vortex lines. By analysing the equilibrium dynamics in the vortex liquid phase we find a dynamic crossover to a glassy non-equilibrium regime. We then focus on the out-of-equilibrium dynamics of the vortex glass phase using tools that are common in the study of other glassy systems. By monitoring the two-times roughness and dynamic wandering we identify and characterize finite-size effects that are similar, though more complex, than the ones found in the stationary roughness of clean interface dynamics. The two-times density-density correlation and mean-squared-displacement correlation age and their temporal scaling follows a multiplicative law similar to the one found at criticality. The linear responses also age and the comparison with their associated correlations shows that the equilibrium fluctuation-dissipation relation is modified in a simple manner that allows for the identification of an effective temperature characterizing the dynamics of the slow modes. The effective temperature is closely related to the vortex liquid-vortex glass crossover temperature. Interestingly enough, our study demonstrates that the glassy dynamics in the vortex glass is basically identical to the one of a single elastic line in a disordered environment (with the same type of scaling though with different parameters). Possible extensions and the experimental relevance of these results are also discussed. 
Sebastian Bustingorry, Leticia F. Cugliandolo, Daniel Dominguez