%0 Journal Article
%T What do we learn from the shape of the dynamical susceptibility of glass-formers?
%+ Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS)
%+ Service de physique de l'état condensé (SPEC - UMR3680)
%+ Laboratoire des colloïdes, verres et nanomatériaux (LCVN)
%+ Service de Physique Théorique (SPhT)
%A Toninelli, Cristina
%A Wyart, Matthieu
%A Berthier, Ludovic
%A Biroli, Giulio
%A Bouchaud, Jean-Philippe
%Z 26 pages, 6 figures
%< avec comité de lecture
%@ 1539-3755
%J Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
%I American Physical Society
%V 71
%P 041505
%8 2005
%D 2005
%Z cond-mat/0412158
%Z Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other]Journal articles
%X 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 an elastic regime characterized by a t or sqrt{t} growth. 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.
%G English
%L hal-00023274
%U https://hal.science/hal-00023274
%~ CEA
%~ ENS-PARIS
%~ UPMC
%~ CNRS
%~ LPTENS
%~ UNIV-MONTP2
%~ LCVN
%~ DSM-IPHT
%~ IRAMIS-SPEC
%~ PSL
%~ UPMC_POLE_2
%~ UNIV-MONTPELLIER
%~ CEA-DRF
%~ SORBONNE-UNIVERSITE
%~ SU-SCIENCES
%~ UP-SCIENCES
%~ ENS-PSL
%~ SU-TI
%~ IRAMIS
%~ GS-PHYSIQUE
%~ ALLIANCE-SU
%~ UM1-UM2