12,063 research outputs found
Asymptotic analysis and spectrum of three anyons
The spectrum of anyons confined in harmonic oscillator potential shows both
linear and nonlinear dependence on the statistical parameter. While the
existence of exact linear solutions have been shown analytically, the nonlinear
dependence has been arrived at by numerical and/or perturbative methods. We
develop a method which shows the possibility of nonlinearly interpolating
spectrum. To be specific we analyse the eigenvalue equation in various
asymptotic regions for the three anyon problem.Comment: 28 pages, LaTeX, 2 Figure
A Fermion-like description of condensed Bosons in a trap
A Bose-Einstein condensate of atoms, trapped in an axially symmetric harmonic
potential, is considered. By averaging the spatial density along the symmetry
direction over a length that preserves the aspect ratio, the system may be
mapped on to a zero temperature noninteracting Fermi-like gas. The ``mock
fermions'' have a state occupancy factor proportional to the ratio of
the coherance length to the ``hard-core'' radius of the atom. The mapping
reproduces the ground state properties of the condensate, and is used to
estimate the vortex excitation energy analytically. The ``mock-fermion''
description predicts some novel collective excitation in the condensed phase.Comment: 11 pages, REVTE
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