We numerically investigate the long-time behavior of the density-density auto-correlation function in driven lattice gases with particle exclusion and periodic boundary conditions in one, two, and three dimensions using precise Monte Carlo simulations. In the one-dimensional asymmetric exclusion process on a ring with half the lattice sites occupied, we find that correlations induce extremely slow relaxation to the asymptotic power law decay. We compare the crossover functions obtained from our simulations with various analytic results in the literature, and analyze the characteristic oscillations that occur in finite systems away from half-filling. As expected, in three dimensions correlations are weak and consequently the mean-field description is adequate. We also investigate the relaxation towards the nonequilibrium steady state in the two-time density-density auto-correlations, starting from strongly correlated initial conditions. We obtain simple aging scaling behavior in one, two, and three dimensions, with the expected power laws.

In order to characterize flux flow through disordered type-II superconductors, we investigate the effects of columnar and point defects on the vortex velocity / voltage power spectrum in the driven non-equilibrium steady state. We employ three-dimensional Metropolis Monte Carlo simulations to measure relevant physical observables including the force-velocity / current-voltage (I-V) characteristics, vortex spatial arrangement and structure factor, and mean flux line radius of gyration. Our simulation results compare well to earlier findings and physical intuition. We focus specifically on the voltage noise power spectra in conjunction with the vortex structure factor in the presence of weak columnar and point pinning centers. We investigate the vortex washboard noise peak and associated higher harmonics, and show that the intensity ratios of the washboard harmonics are determined by the strength of the material defects rather than the type of pins present. Through varying columnar defect lengths and pinning strengths as well as magnetic flux density we further explore the effect of the material defects on vortex transport. It is demonstrated that the radius of gyration displays quantitatively unique features that depend characteristically on the type of material defects present in the sample.

We employ Monte Carlo simulations to study the non-equilibrium relaxation of driven Ising lattice gases in two dimensions. Whereas the temporal scaling of the density auto-correlation function in the non-equilibrium steady state does not allow a precise measurement of the critical exponents, these can be accurately determined from the aging scaling of the two-time auto-correlations and the order parameter evolution following a quench to the critical point. We obtain excellent agreement with renormalization group predictions based on the standard Langevin representation of driven Ising lattice gases.