Einstein relation in superdiffusive systems

Abstract

We study the Einstein relation between diffusion and response to an external field in systems showing superdiffusion. In particular, we investigate a continuous time Levy walk where the velocity remains constant for a time τ, with distribution P(τ) τ^{-g}. At varying g the diffusion can be standard or anomalous; in spite of this, if in the unperturbed system a current is absent, the Einstein relation holds. In the case where a current is present the scenario is more complicated and the usual Einstein relation fails. This suggests that the main ingredient for the breaking of the Einstein relation is not the anomalous diffusion but the presence of a mean drift (current).

10 pages, 3 figures

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Cited by in corpus (7)

• On the Fluctuation-Dissipation Relation in non-equilibrium and non-Hamiltonian systems
• Rare events and scaling properties in field-induced anomalous dynamics
• A no-go theorem for ergodicity and an Einstein relation
• Scaling properties of field-induced superdiffusion in Continous Time Random Walks
• Fluctuation relations without uniform large deviations
• Field-induced superdiffusion and dynamical heterogeneity
• Conservative random walks in confining potentials