Charged and Neutral Vortex Excitations in a Mean Field Theory for the Fractional Quantum Hall Effect

Applying a bi-local mean field approximation to the fractional quantum Hall state of $\nu=1/3$, we obtain charged and neutral vortex mean field solutions numerically. We calculate the mean field energy and the fluctuation corrections. The charged vortex has a fractional charge and a fractional angular momentum. The neutral vortex is a bound state of two charged vortices and has a zero charge and a zero angular momentum. The creation energy of the neutral vortex is about a half of the pair creation energy of two charged vortices. The magnetic field dependence of the gap energy agrees with the Laughlin's quasiparticle gap energy.Comment: 22 pages, EPHOU-94-001, 8 figures available as a hard copy via air-mai

Supernovae in Three-Dimension: A Link to Gamma-Ray Bursts

Observational consequences of a jet-driven supernova (SN) explosion model are presented. The results are compared in detail with optical observations of SN 1998bw associated with a Gamma-Ray Burst. It is shown that the jet model is able to reproduce virtually all the optical observations available for this SN, although a spherical model fails to explain some of observed features. Because of the viewing angle effect, the required kinetic energy of the SN ejecta is reduced to ~ 2 x 10^{52} erg as compared to that obtained by the previous spherical model (~ 5 x 10^{52} erg), but this is still much larger than that of a canonical SN (~10^{51} erg).Comment: 6 pages, 3 figures. Invited talk at "Frascati Workshop 2007: Multifrequency Behaviour of High Energy Cosmic Sources", 28 May - 2 June, 2007, Vulcano, Italy. To apper in the Chinese Journal of Astronomy and Astrophysics (ChJAA

Anisotropy in the Compressible Quantum Hall State

Using a mean field theory on the von Neumann lattice, we study compressible anisotropic states around $\nu=l+1/2$ in the quantum Hall system. The Hartree-Fock energy of the UCDW are calculated self-consistently. In these states the unidirectional charge density wave (UCDW) seems to be the most plausible state. We show that the UCDW is regarded as a collection of the one-dimensional lattice fermion systems which extend to the uniform direction. The kinetic energy of this one-dimensional system is induced from the Coulomb interaction term and the self-consistent Fermi surface is obtained.Comment: 4 pages, to appear in the proceedings of The Tenth International Conference on Recent Progress in Many-Body Theories Seattle, September 10 - 15, 199