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In this paper, we analyze the dynamics of the Coulomb Glass lattice model in three dimensions near a local equilibrium state by using mean-field approximations. We specifically focus on understanding the role of localization length ($\xi$)…
In the framework of schematic hard spheres lattice models we discuss Edwards' Statistical Mechanics approach to granular media. As this approach appears to hold here to a very good approximation, by analytical calculations of Edwards'…
We here discuss the results of 3d MonteCarlo simulations of a minimal lattice model for gelling systems. We focus on the dynamics, investigated by means of the time autocorrelation function of the density fluctuations and the particle mean…
We report a molecular dynamics (MD) study of the collective dynamics of a simple monatomic liquid -interacting through a two body potential that mimics that of lithium- across the liquid-glass transition. In the glassy phase we find…
Slow dynamics in disordered materials prohibits direct simulation of their rich nonequilibrium behavior at large scales. "Patchwork dynamics" is introduced to mimic relaxation over a very broad range of time scales by equilibrating or…
It is known that in systems which contain randomness explicitly in their Hamiltonians (e.g., due to impurities), the characteristic size L of the ordered domains can grow only logarithmically with time t following a quench below the…
We present a systematic study of quantum system compression for the evolution of generic many-body problems. The necessary numerical simulations of such systems are seriously hindered by the exponential growth of the Hilbert space dimension…
We simulate binary soft disk systems in two dimensions, and investigate how the dynamics slow as the area fraction is increased toward the glass transition. The "fragility" quantifies how sensitively the relaxation time scale depends on the…
We study a two-dimensional, off-lattice particle model introduced to describe absorbing phase transitions in driven non-Brownian suspensions. We numerically explore the $(\phi,\epsilon)$ phase diagram, where $\phi$ is the packing fraction…
We study the relation between short-time vibrational modes and long-time relaxational dynamics in a kinetically constrained lattice gas with harmonic interactions between neighbouring particles. We find a correlation between the location of…
The dynamics of glass-forming liquids display several outstanding features, such as two-step relaxation and dynamic heterogeneities, which are difficult to predict quantitatively from first principles. In this work, we revisit a simple…
We explore the effects of spatial locality on the dynamics of random quantum systems subject to a Markovian noise. To this end, we study a model in which the system Hamiltonian and its couplings to the noise are random matrices whose…
We analyze the slow, glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework…
In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second…
The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and…
Amorphous materials exhibit structural heterogeneities that relax only on long timescales. Using machine learning techniques, we construct a Markov state model (MSM) for model glass formers that coarse-grains the dynamics into a…
We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the…
Using simulations we identify three dynamic regimes in supersaturated isotropic fluid states of short hard rods: (i) for moderate supersaturations we observe nucleation of multi-layered crystalline clusters; (ii) at higher supersaturation,…
Glassy dynamics is intermittent, as particles suddenly jump out of the cage formed by their neighbours, and heterogeneous, as these jumps are not uniformly distributed across the system. Relating these features of the dynamics to the…
We show that the main dynamical features of granular media can be understood by means of simple models of fragile-glass forming liquid provided that gravity alone is taken into account. In such lattice-gas models of cohesionless and…