Thermodynamic properties of harmonically trapped D-dimensional ideal gases within generalized exclusion statistics

Abstract

We consider an ideal gas trapped with harmonic potential and obeying the generalized exclusion statistics. We analytically calculate the density of states from which the thermodynamic properties of the gas are calculated for a general energy spectrum ε (p) = a ps in D-dimensional space. Internal energy and the specific heat as a function of temperature are evaluated numerically for different dimensions and energy-momentum dispersion relations. In particular, we show that the specific heat is independent of the statistical parameter g for the constant density of states regime which corresponds D = 1 and s = 2 for this system.