We investigate the relaxation properties of two distinct systems: magnetic vortex lines in disordered type-II superconductors and charge carriers in the Coulomb glass in disordered semiconductors.

We utilize an elastic line model to simulate magnetic flux lines in disordered type-II superconductors by performing Langevin molecular dynamics simulations. We study the non-equilibrium relaxation properties of flux lines in the presence of uncorrelated point-like disorder or extended linear defects analyzing the effects of rapid changes in the system's temperature or magnetic field on these properties. In a previously-equilibrated system, either the temperature is suddenly changed or the magnetic field is abruptly altered by adding or removing random flux lines to or from the system. One-time observables such as the radius of gyration are measured to characterize steady-state properties, and two-time correlation functions such as the vortex line height autocorrelations are computed to investigate the relaxation dynamics in the aging regime and therefore distinguish the complex relaxation features that result from the different types of disorder in the system. This study allows us to test the sensitivity of the system's non-equilibrium aging kinetics to the selection of initial states and to make closer contact to experimental setups.

Furthermore, we employ Monte Carlo simulations to study the relaxation properties of the two-dimensional Coulomb glass in disordered semiconductors and the two-dimensional Bose glass in type-II superconductors in the presence of extended linear defects. We investigate the effects of adding non-zero random on-site energies from different distributions on the properties of the correlation-induced Coulomb gap in the density of states and on the non-equilibrium aging kinetics highlighted by the autocorrelation functions. We also probe the sensitivity of the system's equilibrium and non-equilibrium relaxation properties to instantaneous changes in the density of charge carriers in the Coulomb glass or flux lines in the Bose glass.