# Regensburg 2013 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 31: Anomalous Diffusion

### DY 31.3: Vortrag

### Donnerstag, 14. März 2013, 15:30–15:45, H48

**Spatial-temporal velocity autocorrelation function for random walks.** — •Vasily Zaburdaev^{1}, Sergey Denisov^{2}, and Peter Hänggi^{2} — ^{1}Max Planck Institute for the Physics of Complex Systems, Dresden, Germany — ^{2}Institute of Physics, Augsburg University, Augsburg, Germany

In this work we borrow the concept of spatial-temporal velocity autocorrelation function from the worlds of many-particle systems and fluid dynamics and adopt it for continuous-time random walks. Assuming that at any instant of time a diffusing particle has a well-defined velocity, we pose a question whether it is possible for the particle to remember its initial velocity at some later time and some distance from the starting point. Results are already remarkable for the regime of standard diffusion and exhibit even more rich behavior as diffusion becomes anomalous. We show that for normal diffusion and superdiffusion regimes with sub-ballistic scaling, spatial-temporal velocity autocorrelation function is equivalent to the time derivative of the particle density. As diffusion becomes faster, correlations decay slower in time and might become comparable to the density itself. It is the coupling of displacement and time via a random walker’s velocity that makes a particle to remember its initial velocity far away from the starting point. Spatial-temporal velocity autocorrelation function is an extension of the conventional temporal correlation function for a single particle process and, therefore, provides a new insight into the complex transport phenomena that should find its application in various real world systems.