Tracer Diffusion in Crowded Media

A tracer particle diffusing through a field of fixed obstacles exhibits anomalous subdiffusion: MSD ~ t^α with α < 1 when the obstacle density is high. Near the percolation threshold, diffusion becomes critically slow and tortuous.

MSD(t) = ⟨|r(t)−r(0)|²⟩ ~ D_eff · t^α  |  Normal: α=1  |  Subdiffusion: α<1  |  Percolation threshold φ_c ≈ 0.59