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We study the effect of rapid quench to zero temperature in a model with competing interactions, evolving through conserved spin dynamics. In a certain regime of model parameters, we find that the model belongs to the broader class of kinetically constrained models, however, the dynamics is different from that of a glass. The system shows stretched exponential relaxation with the unusual feature that the relaxation time diverges as a power of the system size. Explicitly, we find that the spatial correlation function decays as $exp(-2r/sqrt{L})$ as a function of spatial separation $r$ in a system with $L$ sites in steady state, while the temporal auto-correlation function follows $exp(-(t/tau_L)^{1/2})$, where $t$ is the time and $tau_L$ proportional to $L$. In the coarsening regime, after time $t_w$, there are two growing length scales, namely $mathcal{L}(t_w) sim t_w^{1/2}$ and $mathcal{R}(t_w) sim t_w^{1/4}$; the spatial correlation function decays as $exp(-r/ mathcal{R}(t_w))$. Interestingly, the stretched exponential form of the auto-correlation function of a single typical sample in steady state differs markedly from that averaged over an ensemble of initial conditions resulting from different quenches; the latter shows a slow power law decay at large times.
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Relaxation in glasses is often approximated by a stretched-exponential form: $f(t) = A exp [-(t/tau)^{beta}]$. Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Corte et al. [Nature Phys. 4, 420 (2008)] can be well approximated by a stretched exponential with an exponent $beta$ that depends on the strain amplitude: $0.25 < beta < 1$. In a one-dimensional version of the model, we show how the relaxation originates from density fluctuations in the initial particle configurations. Our analysis is in good agreement with numerical simulations and reveals a functional form for the relaxation that is distinct from, but well approximated by, a stretched-exponential function.
There are many materials whose dielectric properties are described by a stretched exponential, the so-called Kohlrausch-Williams-Watts (KWW) relaxation function. Its physical origin and statistical-mechanical foundation have been a matter of debate in the literature. In this paper we suggest a model of dielectric relaxation, which naturally leads to a stretched exponential decay function. Some essential characteristics of the underlying charge conduction mechanisms are considered. A kinetic description of the relaxation and charge transport processes is proposed in terms of equations with time-fractional derivatives.
This paper is concerned with the connection between the properties of dielectric relaxation and ac (alternating-current) conduction in disordered dielectrics. The discussion is divided between the classical linear-response theory and a self-consistent dynamical modeling. The key issues are, stretched exponential character of dielectric relaxation, power-law power spectral density, and anomalous dependence of ac conduction coefficient on frequency. We propose a self-consistent model of dielectric relaxation, in which the relaxations are described by a stretched exponential decay function. Mathematically, our study refers to the expanding area of fractional calculus and we propose a systematic derivation of the fractional relaxation and fractional diffusion equations from the property of ac universality.
Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-elastic modulus etc. This behaviour is prominent especially near the glass transition. In this Letter we show, on the example of dielectric relaxation, that stretched-exponential relaxation is intimately related to the peculiar lattice dynamics of glasses. By reformulating the Lorentz model of dielectric matter in a more general form, we express the dielectric response as a function of the vibrational density of states (DOS) for a random assembly of spherical particles interacting harmonically with their nearest-neighbours. Surprisingly we find that near the glass transition for this system (which coincides with the Maxwell rigidity transition), the dielectric relaxation is perfectly consistent with stretched-exponential behaviour with Kohlrausch exponents $0.56 < beta < 0.65$, which is the range where exponents are measured in most experimental systems. Crucially, the root cause of stretched-exponential relaxation can be traced back to soft modes (boson-peak) in the DOS.
We explore phase separation and kinetic arrest in a model active colloidal system consisting of self-propelled, hard-core particles with nonconvex shapes. The passive limit of the model, namely cross-shaped particles on a square lattice, exhibits a first-order transition from a fluid phase to a solid phase with increasing density. Quenches into the two-phase coexistence region exhibit an aging regime. The nonconvex shape of the particles eases jamming in the passive system and leads to strong inhibition of rotations of the active particles. Using numerical simulations and analytical modeling, we quantify the nonequilibrium phase behavior as a function of density and activity. If we view activity as the analog of attraction strength, the phase diagram exhibits strong similarities to that of attractive colloids, exhibiting both aging, glassy states and gel-like arrested states. The two types of dynamically arrested states, glasses and gels, are distinguished by the appearance of density heterogenities in the latter. In the infinitely persistent limit, we show that a coarse-grained model based on the asymmetric exclusion process quantitatively predicts the density profiles of the gel states. The predictions remain qualitatively valid for finite rotation rates. Using these results, we classify the activity-driven phases and identify the boundaries separating them.
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