We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a Levy walk process, often used to
model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.
We study the behavior of a moving wall in contact with a particle gas and subjected to an external force. We compare the fluctuations of the system observed in the microcanonical and canonical ensembles, at varying the number of particles. Static and
dynamic correlations signal significant differences between the two ensembles. Furthermore, velocity-velocity correlations of the moving wall present a complex two-time relaxation which cannot be reproduced by a standard Langevin-like description. Quite remarkably, increasing the number of gas particles in an elongated geometry, we find a typical timescale, related to the interaction between the partitioning wall and the particles, which grows macroscopically.
We study the effect of confinement on glassy liquids using Random First Order Transition theory as framework. We show that the characteristic length-scale above which confinement effects become negligible is related to the point-to-set length-scale i
ntroduced to measure the spatial extent of amorphous order in super-cooled liquids. By confining below this characteristic size, the system becomes a glass. Eventually, for very small sizes, the effect of the boundary is so strong that any collective glassy behavior is wiped out. We clarify similarities and differences between the physical behaviors induced by confinement and by pinning particles outside a spherical cavity (the protocol introduced to measure the point-to-set length). Finally, we discuss possible numerical and experimental tests of our predictions.
We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and glassy ma
terials, and in the Levy walk process, which describes superdiffusion within inhomogeneous media. For both models, in the presence of an external field, rare events induce a singular behavior in the originally Gaussian displacements distribution, giving rise to power-law tails. Remarkably, in the subdiffusive CTRW, the combined effect of highly fluctuating waiting times and of a drift yields a non-Gaussian distribution characterized by long spatial tails and strong anomalous superdiffusion.
Velocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi-2d fluidized granular experiment, with packing fractions $phiin[10%,40%]$. The fluidization is realized by vertically vibrating a rough plat
e, on top of which particles perform a Brownian-like horizontal motion in addition to inelastic collisions. On one hand, the density structure factor is equal to that of elastic hard spheres, except in the limit of large length-scales, as it occurs in the presence of an effective interaction. On the other hand, the velocity field shows a more complex structure which is a genuine expression of a non-equilibrium steady state and which can be compared to a recent fluctuating hydrodynamic theory with non-equilibrium noise. The temporal decay of velocity modes autocorrelations is compatible with linear hydrodynamic equations with rates dictated by viscous momentum diffusion, corrected by a typical interaction time with the thermostat. Equal-time velocity structure factors display a peculiar shape with a plateau at large length-scales and another one at small scales, marking two different temperatures: the bath temperature $T_b$, depending on shaking parameters, and the granular temperature $T_g<T_b$, which is affected by collisions. The two ranges of scales are separated by a correlation length which grows with $phi$, after proper rescaling with the mean free path.
