Non-ergodic diffusion on quenched, scale-free disorder in two dimensions

We discuss our recently introduced models of diffsion on media with random diffusivity~[1] and their application to transport in cell membranes~[2]. We find that the diffusion shows weak ergodicity breaking, and compute the anomalous exponents as a function of model parameters. We also report recent results on criteria for prediciting weak ergodicity breaking in random walks on specific models of quenched, scale-free, random media. \\[4pt] [1] P. Massignan, C. Manzo, J. A. Torreno-Pina, M. F. Garc\'{i}a-Parajo, M. Lewenstein, G. J. Lapeyre, Jr., Phys. Rev. Lett. \textit{112} (2014) \\[0 pt] [2] C. Manzo, J.A. Torreno-Pina, P. Massignan, G.J. Lapeyre Jr., M. Lewenstein, M. F. Garcia-Par\'ajo, arXiv:1407.2552