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Register a new userSlow relaxation and aging kinetics for the driven lattice gas
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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.
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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.
We determine the nonlinear time-dependent response of a tracer on a lattice with randomly distributed hard obstacles as a force is switched on. The calculation is exact to first order in the obstacle density and holds for arbitrarily large forces. Whereas, on the impurity-free lattice, the nonlinear drift velocity in the stationary state is analytic in the driving force, interactions with impurities introduce logarithmic contributions beyond the linear regime. The long-time decay of the velocity toward the steady state is exponentially fast for any finite value of the force, in striking contrast to the power-law relaxation predicted within linear response. We discuss the range of validity of our analytic results by comparison to stochastic simulations.
We present Monte Carlo simulation results on the equilibrium relaxation dynamics in the two dimensional lattice Coulomb gas, where finite fraction $f$ of the lattice sites are occupied by positive charges. In the case of high order rational values of $f$ close to the irrational number $1-g$ ($gequiv(sqrt{5} -1)/2$ is the golden mean), we find that the system exhibits, for wide range of temperatures above the first-order transition, a glassy behavior resembling the primary relaxation of supercooled liquids. Single particle diffusion and structural relaxation show that there exists a breakdown of proportionality between the time scale of diffusion and that of structural relaxation analogous to the violation of the Stokes-Einstein relation in supercooled liquids. Suitably defined dynamic cooperativity is calculated to exhibit the characteristic nature of dynamic heterogeneity present in the system.
We study the relaxation process in a two-dimensional lattice gas model, where the interactions come from the excluded volume. In this model particles have three arms with an asymmetrical shape, which results in geometrical frustration that inhibits full packing. A dynamical crossover is found at the arm percolation of the particles, from a dynamical behavior characterized by a single step relaxation above the transition, to a two-step decay below it. Relaxation functions of the self-part of density fluctuations are well fitted by a stretched exponential form, with a $beta$ exponent decreasing when the temperature is lowered until the percolation transition is reached, and constant below it. The structural arrest of the model seems to happen only at the maximum density of the model, where both the inverse diffusivity and the relaxation time of density fluctuations diverge with a power law. The dynamical non linear susceptibility, defined as the fluctuations of the self-overlap autocorrelation, exhibits a peak at some characteristic time, which seems to diverge at the maximum density as well.
We present results for the fluctuations of the displacement of a tracer particle on a planar lattice pulled by a step force in the presence of impenetrable, immobile obstacles. The fluctuations perpendicular to the applied force are evaluated exactly in first order of the obstacle density for arbitrarily strong pulling and all times. The complex time-dependent behavior is analyzed in terms of the diffusion coefficient, local exponent, and the non-Skellam parameter, which quantifies deviations from the dynamics on the lattice in the absence of obstacles. The non-Skellam parameter along the force is analyzed in terms of an asymptotic model and reveals a power-law growth for intermediate times.
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