Lecture on the anomalous diffusion in Condensed Matter Physics

International audience; Diffusion is a natural or artificial process that governs many phenomena in nature.

The most known diffusion is the Brownian or normal motion, where the mean-square-displacement of the tracer (diffusive particle among others) increases as the square-root of time.

It is not the case, however, for complex systems, where the diffusion is rather slow, because at small-scales, these media present an heterogenous structure.

This kind of slow motion is called subdiffusion, where the associated mean-square-displacement increases in time, with a non trivial exponent, α, whose value is between 0 and 1.

In this review paper, we report on new trends dealt with the study of the anomalous diffusion in Condensed Matter Physics.

The study is achieved using a theoretical approach that is based on a Generalized Langevin Equation.

As particular crowded systems, we choose the so-called Pickering emulsions (oil-in-water), and we are interested in how the dispersed droplets (protected by small solid charged nanoparticles) can diffuse in the continuous phase (water).

Dynamic study is accomplished through the mean-square-displacement and the velocity-autocorrelation-function.

Finally, a comparison with Molecular Dynamics data is made.