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E M Bertin

Publications and source records attributed to E M Bertin.

2 recordsLinked to original sources
PubMed2003

Linear and nonlinear response in the aging regime of the one-dimensional trap model.

We investigate the behavior of the response function in the one-dimensional trap model using scaling arguments that we confirm by numerical simulations. We study the average position of the random walk at time t(w)+t, given that a small bias h is applied at time t(w). Several scaling regimes are found, depending on the relative values of t, t(w), and h. Comparison with the diffusive motion in the absence of bias allows us to show that the fluctuation-dissipation relation is valid even in the aging regime, at least for times such that linear response is obeyed. However, for sufficiently long times, the response always becomes nonlinear in h.

Journal Article↗
PubMed2003

Subdiffusion and localization in the one-dimensional trap model.

We study a one-dimensional generalization of the exponential trap model using both numerical simulations and analytical approximations. We obtain the asymptotic shape of the average diffusion front in the subdiffusive phase. Our central result concerns the localization properties. We find the dynamical participation ratios to be finite, but different from their equilibrium counterparts. Therefore, the idea of a partial equilibrium within the limited region of space explored by the walk is not exact, even for long times where each site is visited a very large number of times. We discuss the physical origin of this discrepancy, and characterize the full distribution of dynamical weights. We also study two different two-time correlation functions, which exhibit different aging properties: one is "sub aging" whereas the other one shows "full aging," therefore, two diverging time scales appear in this model. We give intuitive arguments and simple analytical approximations that account for these differences, and obtain new predictions for the asymptotic (short-time and long-time) behavior of the scaling functions. Finally, we discuss the issue of multiple time scalings in this model.

Journal Article↗