Publication : t04/168
Dynamical susceptibility of glass formers: Contrasting the predictions of theoretical scenarios
Toninelli C. (Ecole Normale Supérieure (ENS), 45, rue d\'Ulm, F-75230 Paris, FRANCE)Wyart M. (CEA, IRAMIS, SPEC (Service de Physique de lEtat Condensé), F-91191 Gif-sur-Yvette, FRANCE)
Berthier L. (Laboratoire des Verres UMR 5587, Univ. Montpellier II et CNRS, pl Eugène Bataillon, F-34090 Montpellier, FRANCE)
Biroli G. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Bouchaud J.-P. (CEA, IRAMIS, SPEC (Service de Physique de lEtat Condensé), F-91191 Gif-sur-Yvette, FRANCE)
Abstract:Année de publication : 2005
We compute analytically and numerically the four-point correlation function that characterizes non-trivial cooperative dynamics in glassy systems within several models of glasses: elasto-plastic deformations, mode-coupling theory (MCT), collectively rearranging regions (CRR), diffusing defects and kinetically constrained models (KCM). Some features of the four-point susceptibility $\chi_4(t)$ are expected to be universal: at short times we expect a power-law increase in time as $t^{4}$ due to ballistic motion ($t^{2}$ if the dynamics is Brownian) followed by an elastic regime (most relevant deep in the glass phase) characterized by a $t$ or $\sqrt{t}$ growth, depending on whether phonons are propagative or diffusive. We find both in the $\beta $, and the early $\alpha $ regime that $\chi_4 \sim t^\mu$, where $\mu$ is directly related to the mechanism responsible for relaxation. This regime ends when a maximum of $\chi_4$ is reached at a time $t=t^*$ of the order of the relaxation time of the system. This maximum is followed by a fast decay to zero at large times. The height of the maximum also follows a power-law, $\chi_4(t^*) \sim t^{*\lambda}$. The value of the exponents $\mu$ and $\lambda$ allows one to distinguish between different mechanisms. For example, freely diffusing defects in $d=3$ lead to $\mu=2$ and $\lambda=1$, whereas the CRR scenario rather predicts either $\mu=1$ or a logarithmic behaviour depending on the nature of the nucleation events, and a logarithmic behaviour of $\chi_4(t^*)$. MCT leads to $\mu=b$ and $\lambda =1/\gamma $, where $b$ and $\gamma$ are the standard MCT exponents. We compare our theoretical results with numerical simulations on a Lennard-Jones and a soft-sphere system. Within the limited time-scales accessible to numerical simulations, we find that the exponent $\mu$ is rather small, $\mu < 1$, with a value in reasonable agreement with the MCT predictions, but not with the prediction of simple diffusive defect models, KCMs with non-cooperative defects and CRR. Experimental and numerical determination of $\chi_4(t)$ for longer time scales and lower temperatures would yield highly valuable information on the glass formation mechanism.
Revue : Phys. Rev. E 71 041505 (2005)
DOI : 10.1103/PhysRevE.71.041505
Preprint : arXiv:cond-mat/0412158
Lien : http://link.aps.org/abstract/PRE/v71/p041505
Numéro Exterieur : SPEC-S04/092
Langue : Anglais
NB : [20 pp.] What do we learn from the shape of the dynamical susceptibility of glass-formers?
Fichier(s) à télécharger :
publi.pdf
