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 $(>>1)$ 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

GALEX Observations of Diffuse UV Radiation at High Spatial Resolution from the Sandage Nebulosity

Using the GALEX ultraviolet imagers we have observed a region of nebulosity first identified as starlight scattered by interstellar dust by Sandage (1976). Apart from airglow and zodiacal emission, we have found a diffuse UV background of between 500 and 800 \phunit in both the \galex FUV (1350 -- 1750 \AA) and NUV (1750 -- 2850 \AA). Of this emission, up to 250 \phunit is due to \htwo fluorescent emission in the FUV band; the remainder is consistent with scattering from interstellar dust. We have estimated the optical constants to be $a = 0.3; g = 0.7$ in the FUV and $a = 0.5; g = 0.7$ in the NUV, implying highly forward scattering grains, plus an extragalactic contribution of as much as 150 \phunit. These are the highest spatial resolution observations of the diffuse UV background to date and show an intrinsic scatter beyond that expected from instrumental noise alone. Further modeling is required to understand the nature of this scatter and its implications for the ISM.Comment: Total 20 pages, Figures 9, Accepted for publication in Astrophysical Journa

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

Classical and Quantum Mechanics of Anyons

We review aspects of classical and quantum mechanics of many anyons confined in an oscillator potential. The quantum mechanics of many anyons is complicated due to the occurrence of multivalued wavefunctions. Nevertheless there exists, for arbitrary number of anyons, a subset of exact solutions which may be interpreted as the breathing modes or equivalently collective modes of the full system. Choosing the three-anyon system as an example, we also discuss the anatomy of the so called ``missing'' states which are in fact known numerically and are set apart from the known exact states by their nonlinear dependence on the statistical parameter in the spectrum. Though classically the equations of motion remains unchanged in the presence of the statistical interaction, the system is non-integrable because the configuration space is now multiply connected. In fact we show that even though the number of constants of motion is the same as the number of degrees of freedom the system is in general not integrable via action-angle variables. This is probably the first known example of a many body pseudo-integrable system. We discuss the classification of the orbits and the symmetry reduction due to the interaction. We also sketch the application of periodic orbit theory (POT) to many anyon systems and show the presence of eigenvalues that are potentially non-linear as a function of the statistical parameter. Finally we perform the semiclassical analysis of the ground state by minimizing the Hamiltonian with fixed angular momentum and further minimization over the quantized values of the angular momentum.Comment: 44 pages, one figure, eps file. References update