Universality and non-universality of mobility in heterogeneous single-file systems and Rouse chains

We study analytically the tracer particle mobility in single-file systems with distributed friction constants. Our system serves as a prototype for non-equilibrium, heterogeneous, strongly interacting Brownian systems. The long time dynamics for such a single-file setup belongs to the same universality class as the Rouse model with dissimilar beads. The friction constants are drawn from a density $\varrho(ξ)$ and we derive an asymptotically exact solution for the mobility distribution $P[μ_0(s)]$, where $μ_0(s)$ is the Laplace-space mobility. If $\varrho$ is light-tailed (first moment exists) we find a self-averaging behaviour: $P[μ_0(s)]=δ[μ_0(s)-μ(s)]$ with $μ(s)\propto s^{1/2}$. When $\varrho(ξ)$ is heavy-tailed, $\varrho(ξ)\simeq ξ^{-1-α} \ (0<α<1)$ for large $ξ$ we obtain moments $\langle [μ_s(0)]^n\rangle \propto s^{βn}$ where $β=1/(1+α)$ and no self-averaging. The results are corroborated by simulations.

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