Dynamics of a one-dimensional "glass" model: Ergodicity and nonexponential relaxation

Strong nonexponential relaxation and memory effects in a fluid with nonlinear drag

We analyze the dynamical evolution of a fluid with nonlinear drag, for which binary collisions are elastic, described at the kinetic level by the Enskog-Fokker-Planck equation. This model system, rooted in the theory of nonlinear Brownian motion, displays a really complex behavior when quenched to low temperatures. Its glassy response is controlled by a long-lived nonequilibrium state, independent of the degree of nonlinearity and also of the Brownian-Brownian collisions rate. The latter property entails that this behavior persists in the collisionless case, where the fluid is described by the nonlinear Fokker-Planck equation. The observed response, which includes nonexponential, algebraic, relaxation, and strong memory effects, presents scaling properties: the time evolution of the temperature-for both relaxation and memory effects-falls onto a master curve, regardless of the details of the experiment. To account for the observed behavior in simulations, it is necessary to develop an extended Sonine approximation for the kinetic equation-which considers not only the fourth cumulant but also the sixth one.

Linear response in the uniformly heated granular gas

We analyze the linear response properties of the uniformly heated granular gas. The intensity of the stochastic driving fixes the value of the granular temperature in the nonequilibrium steady state reached by the system. Here, we investigate two specific situations. First, we look into the "direct" relaxation of the system after a single (small) jump of the driving intensity. This study is carried out by two different methods. Not only do we linearize the evolution equations around the steady state, but we also derive generalized out-of-equilibrium fluctuation-dissipation relations for the relevant response functions. Second, we investigate the behavior of the system in a more complex experiment, specifically a Kovacs-like protocol with two jumps in the driving. The emergence of an anomalous Kovacs response is explained in terms of the properties of the direct relaxation function: it is the second mode changing sign at the critical value of the inelasticity that demarcates anomalous from normal behavior. The analytical results are compared with numerical simulations of the kinetic equation, and a good agreement is found.

Topological solitons in nondegenerate one-component chains

The possibility of the existence of topological solitons in one-component chains with a nondegenerate potential of gradient type is proven. The existence and stability of the solitons are ensured by the competing nonlinear nearest-neighbor potential V1 and parabolic second-nearest-neighbor potential V2. Solitonic solutions have been found analytically for piecewise-parabolic V1 and numerically for smoothened nearest-neighbor (NN) potential V(1,delta). Numerical results for the soliton velocity and front width are in good agreement with analytical estimates. The solitons are shown to move at a unique velocity and actually maintain the constant profile as long as the NN potential is smooth enough. The impact of two solitons of different sign is inelastic and leads to their recombination. It is argued that the soliton propagation may constitute an elementary event of structural transformations in the chain.