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 {\it closed} form for the equation of state at finite temperature, which are both new results. We then solve the problem of particles in a $x^{2/3}$ potential (linear density of states) and show that Bose-Einstein condensation does not occur for any statistics other than bosons.

10 pages (TeX), 2 figures available upon request

References in corpus (2)

• Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics
• Haldane exclusion statistics and second virial coefficient

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• Universal behaviour of ideal and interacting quantum gases in two dimensions
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