The Fermi Statistics of a Weakly Excited Particle in a Vibrating Bed

TL;DR

This study experimentally tests the thermodynamic theory of weakly excited granular systems by fitting density profiles to Fermi distributions and analyzing their temperature-dependent properties, confirming theoretical predictions.

Contribution

It provides experimental validation for the Fermi-Dirac statistical model applied to vibrated granular particles, demonstrating good agreement with theoretical scaling laws.

Findings

Density profiles fit well to Fermi distribution

Measured temperature closely matches predicted values

Scaling behavior of center of mass and fluctuations agrees with theory

Abstract

A one dimensional experiment in granular dynamics is carried out to test the thermodynamic theory of weakly excited granular systems [Hayakawa and Hong, Phys. Rev. Lett. 78, 2764(1997)] where granular particles are treated as spinless Fermions. The density profile is measured and then fit to the Fermi distribution function, from which the global temperature of the system, $T$, is determined. Then the center of mass, $< z(T) >$, and its fluctuations, $< \Delta z(T)^2 >$, are measured and plotted as functions of $T$. The Fermi function fits the density profile fairly well, with the value of $T$ being reasonably close to the predicted value. The scaling behavior of $< z(T) >$ and $< \Delta z(T) ^2 >$ is in excellent agreement with the theory.