It is well known that glass-forming systems display an increase in the maximum of the dynamical susceptibility, which is a feature associated to dynamical heterogeneities, i.e. atoms (or colloids) that move differently in different environments . On the other hand, a model of permanent gels has shown that the dynamical susceptibility is related to the mean cluster size via the critical exponents of percolation theory . Despite this, how general are these findings?
In this work, we examine the dynamical susceptibility for a model that has served for decades as prototype for the description of heterogeneous transport, the Lorentz model . Its non-uniform dynamics is entailed by the presence of point-like intruders that meander a hierarchy of isolated pockets (or clusters) and a percolating fixed matrix.
We thus perform extensive, large-scale Molecular Dynamics simulations of the Lorentz model and find the striking result that, while a diffusion/localisation transition is detected, the dynamical susceptibility does not exceed its typical long-time limit at all wave-vectors. No maximum and no signs of dynamical heterogeneities are observed. To understand these findings, we resort to a specifically designed cluster-resolved theory and compare with cluster-resolved simulations. We discover that only if a sufficiently large fraction of tracers resides on the very same cluster, a susceptibility maximum appears. Consequently, tailored simulations are needed in order to detect the expected increase of heterogeneities. Our outcomes show that the dynamical susceptibility needs to be appropriately treated in order to be a faithful indicator to quantify dynamical heterogeneities.
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