Abstract
Abstract We formulate a scaling theory for the long-time diffusive motion
in a space occluded by a high density of moving obstacles in
dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in
time, before reaching a diffusive steady state with an effective diffusion
constant D eff, which depends on the obstacle diffusivity and density.
The scaling of D eff, above and below a critical regime,
is characterized by two independent critical
parameters: the conductivity exponent μ, also found in models with frozen
obstacles, and an exponent ψ, which quantifies the effect of obstacle
diffusivity.
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