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The long-time behavior of transport coefficients in a model for spatiallyheterogeneous media in two and three dimensions is investigated by MolecularDynamics simulations. The behavior of the velocity auto-correlation function isrationalized in terms of a competition of the critical relaxation due to theunderlying percolation transition and the hydrodynamic power-law anomalies. Intwo dimensions and in the absence of a diffusive mode, another power lawanomaly due to trapping is found with an exponent -3 instead of -2. Further,the logarithmic divergence of the Burnett coefficient is corroborated in thedilute limit; at finite density, however, it is dominated by strongerdivergences.Comment: Full-length paragraph added that exemplifies the relevance for dense  fluids and makes a connection to recently observed, novel long-time tails in  a hard-sphere flui

Crossover in the Slow Decay of Dynamic Correlations in the Lorentz Model