Mode Coupling relaxation scenario in a confined glass former

Molecular dynamics simulations of a Lennard-Jones binary mixture confined in a disordered array of soft spheres are presented. The single particle dynamical behavior of the glass former is examined upon supercooling. Predictions of mode coupling theory are satisfied by the confined liquid. Estimates of the crossover temperature are obtained by power law fit to the diffusion coefficients and relaxation times of the late $\alpha$ region. The $b$ exponent of the von Schweidler law is also evaluated. Similarly to the bulk, different values of the exponent $\gamma$ are extracted from the power law fit to the diffusion coefficients and relaxation times.Comment: 5 pages, 4 figures, changes in the text, accepted for publication on Europhysics Letter

Structural Relaxation and Mode Coupling in a Simple Liquid: Depolarized Light Scattering in Benzene

We have measured depolarized light scattering in liquid benzene over the whole accessible temperature range and over four decades in frequency. Between 40 and 180 GHz we find a susceptibility peak due to structural relaxation. This peak shows stretching and time-temperature scaling as known from $\alpha$ relaxation in glass-forming materials. A simple mode-coupling model provides consistent fits of the entire data set. We conclude that structural relaxation in simple liquids and $\alpha$ relaxation in glass-forming materials are physically the same. A deeper understanding of simple liquids is reached by applying concepts that were originally developed in the context of glass-transition research.Comment: submitted to New J. Phy

Convergence to Stable Laws in Relative Entropy

Convergence to stable laws in relative entropy is established for sums of i.i.d. random variables

Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem

An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.Comment: Published in at http://dx.doi.org/10.1214/12-AOP780 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Mode-Coupling Theory as a Mean-Field Description of the Glass Transition

Mode-coupling theory (MCT) is conjectured to be a mean-field description of dynamics of the structural glass transition and the replica theory to be its thermodynamic counterpart. However, the relationship between the two theories remains controversial and quantitative comparison is lacking. In this Letter, we investigate MCT for monatomic hard sphere fluids at arbitrary dimensions above three and compare the results with replica theory. We find grave discrepancies between the predictions of two theories. While MCT describes the nonergodic parameter quantitatively better than the replica theory in three dimension, it predicts a completely different dimension dependence of the dynamical transition point. We find it to be due to the pathological behavior of the nonergodic parameters derived from MCT, which exhibit negative tails in real space at high dimensions.Comment: 5 pages, to appear in Phys. Rev. Lett.: Typos have been correcte