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Register a new userKovacs Effect in Glass with Material Memory Revealed in Non-Equilibrium Particle Interactions
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The Kovacs effect is a remarkable feature of the ageing dynamics of glass forming liquids near the glass transition temperature. It consists in a non-monotonous evolution of the volume/enthalpy after a succession of two abrupt temperature changes: first from a high initial temperature $T_i$ to a much lower annealing temperature $T_a$ followed by a smaller second jump back to a slightly higher final temperature $T_f$. The second change is performed when the instantaneous value of the volume/enthalpy coincides with the equilibrium one at the final temperature at $t_a$. While this protocol might be expected to yield equilibrium dynamics right after the second temperature change, one observes the so-called Kovacs hump in glassy systems. In this paper we apply such thermal protocol to the Distinguishable Particles Lattice Model (DPLM) for a wide range of fragility of the system. We study the Kovacs hump based on energy relaxation and all main experimental features are captured. Results are compared to general predictions based on a master equation approach in the linear response limit. We trace the origin of the Kovacs hump to the non-equilibrium nature of the probability distribution of particle interaction energies after the annealing and find that its difference with respect to the final equilibrium distribution is non-vanishing with two isolated zeros. This allows Kovacs condition of equilibrium total energy to be met out-of-equilibrium thus representing the memory content of the system. Furthermore, the hump is taller and occurs at a larger overlap with the system initial configuration for more fragile systems. The dynamics of a structural temperature for the mobile regions strongly depends on the glass fragility while for the immobile ones only a weak dependence is found.
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Volume and enthalpy relaxation of glasses after a sudden temperature change has been extensively studied since Kovacs seminal work. One observes an asymmetric approach to equilibrium upon cooling versus heating and, more counter-intuitively, the expansion gap paradox, i.e. a dependence on the initial temperature of the effective relaxation time even close to equilibrium when heating. Here we show that a distinguishable-particles lattice model can capture both the asymmetry and the expansion gap. We quantitatively characterize the energetic states of the particles configurations using a physical realization of the fictive temperature called the structural temperature, which, in the heating case, displays a strong spatial heterogeneity. The system relaxes by nucleation and expansion of warmer mobile domains having attained the final temperature, against cooler immobile domains maintained at the initial temperature. A small population of these cooler regions persists close to equilibrium, thus explaining the paradox.
We analyse the emergence of Kovacs-like memory effects in athermal systems within the linear response regime. This is done by starting from both the master equation for the probability distribution and the equations for the physically relevant moments. The general results are applied to a general class of models with conserved momentum and non-conserved energy. Our theoretical predictions, obtained within the first Sonine approximation, show an excellent agreement with the numerical results.
Athermal systems across a large range of length scales, ranging from foams and granular bead packings to crumpled metallic sheets, exhibit slow stress relaxation when compressed. Experimentally they show a non-monotonic stress response when decompressed somewhat after an initial compression, i.e. under a two-step, Kovacs-like protocol. It turns out that from this response one can tell the age of the system, suggesting an interpretation as a memory effect. In this work we use a model of an athermal jammed solid, specifically a binary mixture of soft harmonic spheres, to explore this phenomenon through in-silico experiments. Using extensive simulations under conditions analogous to those in experiment, we observe identical phenomenology in the stress response under a two--step protocol. Our model system also recovers the behaviour under a more recently studied three-step protocol, which consists of a compression followed by a decompression and then a final compression. We show that the observed response in both two-step and three-step protocols can be understood using Linear Response Theory. In particular, a linear scaling with age for the two-step protocol arises generically for slow linear responses with power law or logarithmic decay and does not in itself point to any underlying aging dynamics.
The interplay of fluctuations, ergodicity, and disorder in many-body interacting systems has been striking attention for half a century, pivoted on two celebrated phenomena: Anderson localization predicted in disordered media, and Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence observed in a nonlinear system. The destruction of Anderson localization by nonlinearity and the recovery of ergodicity after long enough computational times lead to more questions. This thesis is devoted to contributing to the insight of the nonlinear system dynamics in and out of equilibrium. Focusing mainly on the GP lattice, we investigated elementary fluctuations close to zero temperature, localization properties, the chaotic subdiffusive regimes, and the non-equipartition of energy in non-Gibbs regime. Initially, we probe equilibrium dynamics in the ordered GP lattice and report a weakly non-ergodic dynamics, and an ergodic part in the non-Gibbs phase that implies the Gibbs distribution should be modified. Next, we include disorder in GP lattice, and build analytical expressions for the thermodynamic properties of the ground state, and identify a Lifshits glass regime where disorder dominates over the interactions. In the opposite strong interaction regime, we investigate the elementary excitations above the ground state and found a dramatic increase of the localization length of Bogoliubov modes (BM) with increasing particle density. Finally, we study non-equilibrium dynamics with disordered GP lattice by performing novel energy and norm density resolved wave packet spreading. In particular, we observed strong chaos spreading over several decades, and identified a Lifshits phase which shows a significant slowing down of sub-diffusive spreading.
The sluggish and heterogeneous dynamics of glass forming liquids is frequently associated to the transient coexistence of two phases of particles, respectively with an high and low mobility. In the absence of a dynamical order parameter that acquires a transient bimodal shape, these phases are commonly identified empirically, which makes difficult investigating their relation with the structural properties of the system. Here we show that the distribution of single particle diffusivities can be accessed within a Continuous Time Random Walk description of the intermittent motion, and that this distribution acquires a transient bimodal shape in the deeply supercooled regime, thus allowing for a clear identification of the two coexisting phase. In a simple two-dimensional glass forming model, the dynamic phase coexistence is accompanied by a striking structural counterpart: the distribution of the crystalline-like order parameter becomes also bimodal on cooling, with increasing overlap between ordered and immobile particles. This simple structural signature is absent in other models, such as the three-dimesional Kob-Andersen Lennard-Jones mixture, where more sophisticated order parameters might be relevant. In this perspective, the identification of the two dynamical coexisting phases opens the way to deeper investigations of structure-dynamics correlations.
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