SFB 1551 Seminar Series Event – Prof. Dr. Ralf Metzler

Talk announcement for Prof. Dr. Ralf Metzler.

“Long-ranged correlated processes in disordered systems”

By Prof. Dr. Ralf Metzler

Universität Potsdam

Abstract from Prof. Metzler:

Stochastic processes with long-ranged, power-law correlations naturally emerge in systems such as Rouse polymers or single-file systems, when all degrees of freedom are integrated out, apart from the (tracer) particle of interest. In non-equilibrium situations, the resulting overdamped dynamics corresponds to Mandelbrot’s fractional Brownian motion (FBM).

This talk will address some peculiar behaviours of FBM when subject to confinement in box potentials as well as sub- or superharmonic external potentials. Specifically, it will be argued why superdiffusive FBM may be a good (polymer) model for growing serotonergic fibres in the mammalian brain.

In disordered environments it will be shown how non-Gaussian displacement density functions emerge and subtly depend on how the dynamics is introduced. This is achieved by stochastic-diffusivity models connected with long-range dependent noise. Moreover, it will be discussed how time-dependent critical exponents can be introduced in this formalism.

Finally, amoeba systems will be introduced in which the displacement density function appears to converge to a non-Gaussian, Laplace density.