We investigate theoretically the slow non-exponential relaxation dynamics of the electron glass out of equilibrium, where a sudden change in carrier density reveals interesting memory effects. The self-consistent model of the dynamics of the occupati
on numbers in the system successfully recovers the general behavior found in experiments. Our numerical analysis is consistent with both the expected logarithmic relaxation and our understanding of how increasing disorder or interaction slows down the relaxation process, thus yielding a consistent picture of the electron glass. We also present a novel finite size domino effect where the connection to the leads affects the relaxation process of the electron glass in mesoscopic systems. This effect speeds up the relaxation process, and even reverses the expected effect of interaction; stronger interaction then leading to a faster relaxation.
Experiments on particles motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading to continuou
s-time random walks) can easily be distinguished from the rest by testing their non-ergodicity, the latter two cases are harder to distinguish. We propose a statistical test for distinguishing between these two based on the space-filling properties of trajectories, and prove its feasibility and specificity using synthetic data. We moreover present a flow-chart for making a decision on a type of subdiffusion for a broader class of models.
It is the common lore to assume that knowing the equation for the probability distribution function (PDF) of a stochastic model as a function of time tells the whole picture defining all other characteristics of the model. We show that this is not th
e case by comparing two exactly solvable models of anomalous diffusion due to geometric constraints: The comb model and the random walk on a random walk (RWRW). We show that though the two models have exactly the same PDFs, they differ in other respects, like their first passage time (FPT) distributions, their autocorrelation functions and their aging properties.
