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Fluctuations in glassy systems

Glassy dynamics occur out of equilibrium with special properties such as physical aging, memory effects and dynamic heterogeneities, that is to say, regions of particles rearranging cooperatively at the nanometer scale, at very different rates compared with the bulk. Such features have been observed in a wide variety of
materials including vortex matter in high-Tc superconductors.
The symmetry that captures the universal fluctuating aging dynamics of glassy systems should be the invariance of an effective dynamical action under uniform reparametrizations of the time-scales.
This scenario was put to the test with Monte Carlo simulations of the 3d
Edwards-Anderson spin-glass, the 3d random field Ising model, and confocal
microscopy data on dense (super-cooled liquid and glassy) colloidal suspensions.
We constructed restricted averages to obtain objects with a better statistics than the
completely fluctuating ones. The outcome of these studies is that while truly glassy systems conform to the consequences of the hypothesis, simple coarsening does not with time-reparametrization invariance being reduced to time rescaling at the heart of the difference. This result suggests that the fluctuations are intimately related to the global effective temperature.
A directed elastic manifold in random media is a system with many glassy aspects due to the competition between elasticity and disorder. The study of the Edwards-Wilkinson and a disordered elastic line, confirmed the growth of a coherence length that controls the scaling properties of averaged observables. A set of regimes going from normal diffusive aging to saturation -a la Family-Vicsek for finite-length lines passing through activated aging have been exhibited. The fluctuations of two-time quantities behave has also been analyzed.
As a first step towards a successful field theory of Brownian particles in interaction, we studied exactly the Brownian gas. Even though the particles do not interact, the field theory contains an interaction term that enforce the constraint of a strictly positive density field. In this paper we determined non-perturbatively the Poissonian nature of the ground state.