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.
We study the nonequilibrium aging dynamics in a system of quasi-hard spheres at large density by means of computer simulations. We find that, after a sudden quench to large density, the relaxation time initially increases exponentially with the age of the system. After a surprisingly large crossover time, the system enters the asymptotic aging regime characterized by a linear increase of the relaxation time with age. In this aging regime, single particle motion is strongly non-Fickian, with a mean-squared displacement increasing subdiffusively, associated to broad, non-Gaussian tails in the di…
We numerically investigate the stationary and non-equilibrium critical dynamics in three-dimensional isotropic Heisenberg antiferromagnets. Since the non-conserved staggered magnetization couples dynamically to the conserved magnetization density, we employ a hybrid simulation algorithm that combines reversible spin precession with relaxational Kawasaki spin exchange processes. We measure the dynamic critical exponent and identify a suitable intermediate time window to obtain the aging scaling exponents. Our results support an earlier renormalization group prediction: While the critical aging …
The complex Ginzburg-Landau equation with additive noise is a stochastic partial differential equation that describes a remarkably wide range of physical systems which include coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability and spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations or oscillatory chemical reactions. We employ a finite-difference method to numerically solve the noisy complex Ginzburg-Landau equation on a two-dimensional domain with the goal to investigate its non-equilibrium dynamics whe…
Dynamical Mean-Field Theory (DMFT) replaces the many-body dynamical problem with one for a single degree of freedom in a thermal bath whose features are determined self-consistently. By focusing on models with soft disordered $p$-spin interactions, we show how to incorporate the mean-field theory of aging within dynamical mean-field theory. We study cases with only one slow time-scale, corresponding statically to the one-step replica symmetry breaking (1RSB) phase, and cases with an infinite number of slow time-scales, corresponding statically to the full replica symmetry breaking (FRSB) phase…
We study the thermal effects on the frictional properties of atomically thin sheets. We simulate a simple model based on the Prandtl-Tomlinson model that reproduces the layer dependence of friction and strengthening effects seen in AFM experiments. We investigate sliding at constant speed as well as reversing direction. We also investigate contact aging: the changes that occur to the contact when the sliding stops completely. We compare the numerical results to analytical calculations based on Kramers rates. We find that there is a slower than exponential contact aging that weakens the contact…
We utilize Langevin molecular dynamics simulations to study dynamical critical behavior of magnetic flux lines near the depinning transition in type-II superconductors subject to randomly distributed attractive point defects. We employ a coarse-grained elastic line Hamiltonian for the mutually repulsive vortices and purely relaxational kinetics. In order to infer the stationary-state critical exponents for the continuous non-equilibrium depinning transition at zero temperature T = 0 and at the critical driving current density j_c, we explore two-parameter scaling laws for the flux lines' gyrat…
We analyze the late-time relaxation dynamics for a general contagion model. In this model, nodes are either active or failed. Active nodes can fail either "spontaneously" at any time or "externally" if their neighborhoods are sufficiently damaged. Failed nodes may always recover spontaneously. At late times, the breaking of time-translation-invariance is a necessary condition for physical aging. We observe that time-translational invariance is lost for initial conditions that lie between the basins of attraction of the model's two stable stationary states. Based on corresponding mean-field pre…
Many experiments show that protein condensates formed by liquid-liquid phase separation exhibit aging rheological properties. Quantitatively, recent experiments by Jawerth et al. (Science 370, 1317, 2020) show that protein condensates behave as aging Maxwell fluids with an increasing relaxation time as the condensates age. Despite the universality of this aging phenomenon, a theoretical understanding of this aging behavior is lacking. In this work, we propose a mesoscopic model of protein condensates in which a phase transition from aging phase to non-aging phase occurs as the control paramete…
Although it has been known for half a century that the physical aging of glasses in experiments is described well by a linear thermal-history convolution integral over the so-called material time, the microscopic definition and interpretation of the material time remains a mystery. We propose that the material-time increase over a given time interval reflects the distance traveled by the system's particles. Different possible distance measures are discussed, starting from the standard mean-square displacement and its inherent-state version that excludes the vibrational contribution. The viewpo…
