Fermi-statistics in the real space

Granular matter (GM) is a paradigm system for investigating   various complexities of dissipative non-equilibrium systems. When a   sand box is shaken, the grains in the upper layer start jumping   resembling "evaporation", and the transition to gas phase begins at the upper surface of the GM. One of the interesting aspects of this gas phase is the deviation from Maxwell velocity distribution.  Furthermore, the grains in the bulk exhibit cooperative non-Brownian behavior.

A laser facility based on a linear image sensor with a sampling period of 100 µs allows the investigation of the dissipative dynamics of a vibrated GM under gravity. The stochastic realizations are measured from the top of the container. Then, power spectra of measurements reveal the different cooperative dynamics of the fluidized gap. Our studies are shown that the system obeys a Fermi-like  statistics in the real space. This analogy to quantum particles is a consequence of the volume exclusion principle and is the key   element for describing a weakly vibrated GM under gravity. Our studies led to a successful definition of a GM global temperature and resulted in a generalized equipartition law for GM. We have established a quantitative link between the configurational entropy and the response of the system.

From this basic experimental research on the Fermi-like statistics in the real space we expect to get important insight into the physics of condensed matter and complex fluids. 

This work was done in the group of Prof. Christian Wagner at the Universitaet des Saarlandes, Germany.