Fermi Statistics of Weakly Excited Granular Materials in a Vibrating Bed II: One Dimensional Experiment

TL;DR

This study experimentally tests the thermodynamic theory of weakly excited granular materials by fitting density profiles to Fermi distributions and analyzing their temperature-dependent properties in a one-dimensional vibrating bed.

Contribution

It provides experimental validation of the Fermi-Dirac statistical model for granular systems and confirms theoretical predictions of their thermodynamic behavior.

Findings

Fermi distribution fits the density profile well

Measured temperature closely matches theoretical predictions

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. {\bf 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 fairly close to the predicted value. The scaling behavior of <z(T)> and <(\Delta z(T))^2> is in excellent agreement with the theory.