Universality and nonuniversality 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 nonequilibrium, 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 rho(xi), and we derive an asymptotically exact solution for the mobility distribution P[mu(0)(s)], where mu(0)(s) is the Laplace-space mobility. If rho is light tailed (first moment exists), we find a self-averaging behavior: P[mu(0)(s)] = delta[mu(0)(s) - mu(s)], with mu(s) alpha s(1/2). When rho(xi) is heavy tailed, rho(xi) similar or equal to xi(-1-alpha) (0 < alpha < 1) for large xi, we obtain moments <[mu(s)(0)(n)]> alpha s(beta n), where beta = 1/(1 + alpha) and there is no self-averaging. The results are corroborated by simulations.