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arXiv:cond-mat/9902158

A two-dimensional interacting system obeying Fractional Exclusion Statistics

M. K. Srivastava, R. K. Bhaduri, J. Law, M. V. N. Murthy

Published Feb 11, 1999• 0 citations
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Abstract

We consider N fermions in a two-dimensional harmonic oscillator potential interacting with a very short-range repulsive pair-wise potential. The ground-state energy of this system is obtained by performing a Thomas-Fermi as well as a self-consistent Hartree-Fock calculation. The two results are shown to agree even for a small number of particles. We next use the finite temperature Thomas-Fermi method to demonstrate that in the local density approximation, these interacting fermions are equivalent to a system of noninteracting particles obeying the Haldane-Wu fractional exclusion statistics. It is also shown that mapping onto to a system of N noninteracting quasi-particles enables us to predict the energies of the excited states of the N-body system.

DOI
10.48550/arxiv.cond-mat/9902158

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We describe a mean field interacting particle system in any number of dimensions and in a generic external potential as an ideal gas with fractional exclusion statistics (FES). We define the FES quasiparticle energies, we calculate the FES parameters of the system and we deduce the equations for the equilibrium particle populations. The FES gas is "ideal," in the sense that the quasiparticle energies do not depend on the other quasiparticle levels' populations and the sum of the quasiparticle energies is equal to the total energy of the system. We prove that the FES formalism is equivalent to the semiclassical or Thomas Fermi limit of the self-consistent mean-field theory and the FES quasiparticle populations may be calculated from the Landau quasiparticle populations by making the correspondence between the FES and the Landau quasiparticle energies. The FES provides a natural semiclassical ideal gas description of the interacting particle gas.