Diffusion in Two-Dimensional Hyperuniform Media

Understanding diffusion in disordered systems composed of obstacle particles is crucial for elucidating transport phenomena ranging from biological tissues to engineered porous materials. Existing studies predominantly employ the random sequential adsorption method and characterize media solely by density ρ. We show that this is fundamentally incomplete: These structures exhibit a tunable hyperuniformity exponent β that spans from periodic lattices to Poisson processes, yielding qualitatively different diffusion even at identical ρ. We derive a β-dependent analytical expression for the diffusion coefficient 1-D/D_{0}∼ρ^{2-β/2} in the low-ρ limit and predict a β-dependent percolation threshold ρ_{c}(β) in the high-ρ regime. Brownian dynamics simulations across the full (β,ρ) plane complete the picture, yielding both the diffusion coefficients and the phase diagram of normal, hopping, and trapped states.