Field-induced superdiffusion and dynamical heterogeneity

Abstract

By analyzing two Kinetically Constrained Models of supercooled liquids we show that the anomalous transport of a driven tracer observed in supercooled liquids is another facet of the phenomenon of dynamical heterogeneity. We focus on the Fredrickson-Andersen and the Bertin-Bouchaud-Lequeux models. By numerical simulations and analytical arguments we demonstrate that the violation of the Stokes-Einstein relation and the observed field-induced superdiffusion have the same physical origin: while a fraction of probes do not move, others jump repeatedly because they are close to local mobile regions. The anomalous fluctuations observed out of equilibrium in presence of a pulling force $\epsilon$, ${\sigma }_x^2(t)=⟨x_{\epsilon }^2(t)⟩-⟨x_{\epsilon }(t){⟩}^2\sim t^{3/2}$, which are accompanied by the asymptotic decay ${\alpha }_{\epsilon }(t)\sim t^{-1/2}$ of the non-Gaussian parameter from non-trivial values to zero, are due to the splitting of the probes population in the two (mobile and immobile) groups and to dynamical correlations, a mechanism expected to happen generically in supercooled liquids.

5 pages, 2 figures

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• Dynamics and friction of a large colloidal particle in a bath of hard spheres: Langevin dynamics simulations and hydrodynamic description
• Simulation of the continuous-time random walk using subordination schemes