Non-linear Response of the trap model in the aging regime : Exact results in the strong disorder limit

Abstract

We study the dynamics of the one dimensional disordered trap model presenting a broad distribution of trapping times $p(\tau )\sim 1/{\tau }^{1+\mu }$, when an external force is applied from the very beginning at $t=0$, or only after a waiting time $t_w$, in the linear as well as in the non-linear response regime. Using a real-space renormalization procedure that becomes exact in the limit of strong disorder $\mu \to 0$, we obtain explicit results for many observables, such as the diffusion front, the mean position, the thermal width, the localization parameters and the two-particle correlation function. In particular, the scaling functions for these observables give access to the complete interpolation between the unbiased case and the directed case. Finally, we discuss in details the various regimes that exist for the averaged position in terms of the two times and the external field.

27 pages, 1 eps figure

References in corpus (4)

• Sub-diffusion and localization in the one dimensional trap model
• Anomalous diffusion, Localization, Aging and Sub-aging effects in trap models at very low temperature
• Localization properties of the anomalous diffusion phase $x{t}^{\mu }$ in the directed trap model and in the Sinai diffusion with bias
• Linear and non linear response in the aging regime of the 1D trap model

Cited by in corpus (23)

• Strong disorder RG approach of random systems
• Dynamics of trap models
• Large Deviations for the density and the current in Non-Equilibrium-Steady-States on disordered rings
• Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models
• Random walks and polymers in the presence of quenched disorder
• Dynamical transition for a particle in a squared Gaussian potential
• Non equilibrium dynamics of disordered systems : understanding the broad continuum of relevant time scales via a strong-disorder RG in configuration space
• Random elastic networks : strong disorder renormalization approach
• From Quenched Disorder to Continuous Time Random Walk
• Equilibrium of disordered systems : constructing the appropriate valleys in each sample via strong disorder renormalization in configuration space
• Strong Disorder Renormalization for the dynamics of Many-Body-Localized systems : iterative elimination of the fastest degree of freedom via the Floquet expansion
• Random walk in two-dimensional self-affine random potentials : strong disorder renormalization approach
• The case of the biased quenched trap model in two dimensions with diverging mean dwell times
• Non-equilibrium dynamics of finite-dimensional disordered systems : RG flow towards an "infinite disorder" fixed point at large times
• Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?
• Duality between random trap and barrier models
• Scaling limit and aging for directed trap models
• Statistics of first-passage times in disordered systems using backward master equations and their exact renormalization rules
• The Transient Case of The Quenched Trap Model
• Finite-size effects and intermittency in a simple aging system
• Trap models with vanishing drift: Scaling limits and aging regimes
• On the Kemeny time for continuous-time reversible and irreversible Markov processes with applications to stochastic resetting and to conditioning towards forever-survival
• Markov dualities via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors