Scarce defects induce anomalous diffusion

  title={Scarce defects induce anomalous diffusion},
  author={M. Hidalgo-Soria and R. Salgado-Garc'ia},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
We introduce a simple model of deterministic particles in weakly disordered media which exhibits a transition from normal to anomalous diffusion. The model consists of a set of non-interacting overdamped particles moving on a disordered potential. The disordered potential can be thought as a substrate having some ‘defects’ scattered along a one-dimensional line. The distance between two contiguous defects is assumed to have a heavy-tailed distribution with a given exponent α, which means that… 

Figures from this paper

Noise-induced rectification in out-of-equilibrium structures.

It is shown that the net flux of particles over this random medium is nonvanishing when the potential profile on every monomer is symmetric, and it is proved that this ratchetlike phenomenon is a consequence of the irreversibility of the stochastic process generating the polymer.

Freezing phase transition in a fractal potential

It is proved that below the critical temperature the Gibbs–Boltzmann probability measure is supported on the middle-third Cantor set and that further lowering the temperature, the probability measure does not change anymore, indicating that the system ‘freezes’ at a positive temperature.



Normal-to-anomalous diffusion transition in disordered correlated potentials: from the central limit theorem to stable laws.

It is found that the diffusion properties of such a system are closely related to the correlation function of the corresponding potential, and model the substrate as a symbolic trajectory of a shift space which enables a general formula for the diffusion coefficient when normal diffusion occurs.

Effective diffusion coefficient in tilted disordered potentials: optimal relative diffusivity at a finite temperature.

  • R. Salgado-García
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2014
This work studies the transport properties of non-interacting overdamped particles, moving on tilted disordered potentials, subjected to Gaussian white noise, and finds that the diffusion coefficient exhibits a non-monotonous behavior as a function of the noise intensity.

Mechanical model of normal and anomalous diffusion.

The results exemplify that, even in the absence of time-dependent stochastic forces, a purely mechanical model equipped with a quenched disorder can exhibit normal as well as anomalous diffusion, the latter emerging as a critical property.


Particles driven through a periodic potential by an external constant force are known to exhibit a pronounced peak of the diffusion around the critical deterministic force that defines the transition


We consider anomalous non-Markovian transport of Brownian particles in viscoelastic fluid-like media with very large but finite macroscopic viscosity under the influence of a constant force field F.

Unbiased diffusion of Brownian particles on disordered correlated potentials

In this work we study the diffusion of non-interacting overdamped particles, moving on unbiased disordered correlated potentials, subjected to Gaussian white noise. We obtain an exact expression for

Transport and diffusion of underdamped Brownian particles in random potentials

We present numerical results for the transport and diffusion of underdamped Brownian particles in one-dimensional disordered potentials. We compare the anomalies observed with those found in the

Biased diffusion in a piecewise linear random potential

AbstractWe study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation