Scaling study of diffusion in dynamic crowded spaces

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 $D_{\mathrm{eff}}$, which depends on the obstacle diffusivity and density. The scaling of $D_{\mathrm{eff}}$, above and below a critical regime, is characterized by two independent critical parameters: the conductivity exponent $\hat{I}¼$, also found in models with frozen obstacles, and an exponent $\ddot{I}ˆ$, which quantifies the effect of obstacle diffusivity.

Version accepted for publication in J. Phys. A. 13 pages, 7 figures