Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics

Details Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics

1994-11-17

arxiv.org/abs/cond-mat/9411073v1

Physics

Condensed Matter

10 pages (TeX), 2 figures available upon request

Scientific paper

10.1103/PhysRevLett.74.3912

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.

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