Field-induced superdiffusion and dynamical heterogeneity

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 ϵ, σ2x(t)=⟨x2ϵ(t)⟩−⟨xϵ(t)⟩2∼t3/2, which are accompanied by the asymptotic decay αϵ(t)∼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.