# Scarce defects induce anomalous diffusion

@article{HidalgoSoria2016ScarceDI, title={Scarce defects induce anomalous diffusion}, author={M. Hidalgo-Soria and R. Salgado-Garc'ia}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2016}, volume={2017} }

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…

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## References

SHOWING 1-10 OF 19 REFERENCES

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

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

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.

- MathematicsPhysical 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.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

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.

### WEAK DISORDER IN PERIODIC POTENTIALS: ANOMALOUS TRANSPORT AND DIFFUSION

- Physics
- 2012

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…

### Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications

- Physics
- 1990

### IS SUBDIFFUSIONAL TRANSPORT SLOWER THAN NORMAL

- Physics
- 2012

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

- Mathematics
- 2015

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

- PhysicsThe European Physical Journal B
- 2014

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

- Mathematics
- 2010

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…