Few-anyon systems in a parabolic dot

The energy levels of two and three anyons in a two-dimensional parabolic quantum dot and a perpendicular magnetic field are computed as power series in 1/|J|, where J is the angular momentum. The particles interact repulsively through a coulombic (1/r) potential. In the two-anyon problem, the reached accuracy is better than one part in 10^5. For three anyons, we study the combined effects of anyon statistics and coulomb repulsion in the ``linear'' anyonic states.Comment: LaTeX, 6 pages, 4 postscript figure

Approximate formula for the ground state energy of anyons in 2D parabolic well

We determine approximate formula for the ground state energy of anyons in 2D parabolic well which is valid for the arbitrary anyonic factor \nu and number of particles N in the system. We assume that centre of mass motion energy is not excluded from the energy of the system. Formula for ground state energy calculated by variational principle contains logarithmic divergence at small distances between two anyons which is regularized by cut-off parameter. By equating this variational formula to the analogous formula of Wu near bosonic limit (\nu ~ 0)we determine the value of the cut-off and thus derive the approximate formula for the ground state energy for the any \nu and N. We checked this formula at \nu=1, when anyons become fermions, for the systems containing two to thirty particles. We find that our approximate formula has an accuracy within 6%. It turns out, at the big number N limit the ground state energy has square root dependence on factor \nu.Comment: 7 page

W infinity-covariance of the Weyl-Wigner-Groenewold-Moyal quantization

The differential structure of operator bases used in various forms of the Weyl-Wigner-Groenewold-Moyal (WWGM) quantization is analyzed and a derivative-based approach, alternative to the conventional integral-based one is developed. Thus the fundamental quantum relations follow in a simpler and unified manner. An explicit formula for the ordered products of the Heisenberg-Weyl algebra is obtained. The W-infinity-covariance of the WWGM-quantization in its most general form is established. It is shown that the group action of W-infinity that is realized in the classical phase space induces on bases operators in the corresponding Hilbert space a similarity transformation generated by the corresponding quantum W-infinity which provides a projective representation of the former W-infinity. Explicit expressions for the algebra generators in the classical phase space and in the Hilbert space are given. It is made manifest that this W-infinity-covariance of the WWGM-quantization is a genuine property of the operator bases. (C) 1997 American Institute of Physics