Anomalous diffusion and response in branched systems: a simple analysis

Abstract

We revisit the diffusion properties and the mean drift induced by an external field of a random walk process in a class of branched structures, as the comb lattice and the linear chains of plaquettes. A simple treatment based on scaling arguments is able to predict the correct anomalous regime for different topologies. In addition, we show that even in the presence of anomalous diffusion, Einstein's relation still holds, implying a proportionality between the mean square displacement of the unperturbed systems and the drift induced by an external forcing.

revtex.4-1, 16 pages, 7 figures

References in corpus (3)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• On anomalous diffusion and the out of equilibrium response function in one-dimensional models
• Normal and Anomalous Fluctuation Relations for Gaussian Stochastic Dynamics

Cited by in corpus (11)

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• Mesoscopic description of random walks on combs
• Langevin dynamics for ramified structures
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• Anomalous mobility of a driven active particle in a steady laminar flow
• The effect of the junction model on the anomalous diffusion in the 3D comb structure
• Richardson diffusion in neurons
• Transport and fluctuation-dissipation relations in asymptotic and pre-asymptotic diffusion across channels with variable section
• Random walks on uniform and non-uniform combs and brushes
• Asymptotic versus mesoscopic spectral dimensions in networks and inhomogeneous structures
• Destruction of ultra-slow diffusion in a three dimensional cylindrical comb structure