Thomas-Fermi method for particles obeying generalized exclusion statistics

Abstract

We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a simple harmonic potential (constant density of states), we obtain the exact one-particle spatial density and a closed form for the equation of state at finite temperature, which are both new results. We then solve the problem of particles in a x^⅔ potential (linear density of states) and show that Bose-Einstein condensation does not occur for any statistics other than bosons.