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

Nonautonomous ultradiscrete hungry Toda lattice and a generalized box-ball system

A nonautonomous version of the ultradiscrete hungry Toda lattice with a finite lattice boundary condition is derived by applying reduction and ultradiscretization to a nonautonomous two-dimensional discrete Toda lattice. It is shown that the derived ultradiscrete system has a direct connection to the box-ball system with many kinds of balls and finite carrier capacity. Particular solutions to the ultradiscrete system are constructed by using the theory of some sort of discrete biorthogonal polynomials.Comment: 28 pages, 4 figure

Flux State in von Neumann lattice and Fractional Hall Effect

Formulation of quantum Hall dynamics using von Neumann lattice of guiding center coordinates is presented. A topological invariant expression of the Hall conductance is given and a new mean field theory of the fractional Hall effect based on flux condensation is proposed. Because our mean field Hamiltonian has the same form as Hofstadter Hamiltonian, it is possible to understand characteristic features of the fractional Hall effect from Hofstadter's spectrum. Energy gap and other physical quantities are computed and are compared with the experiments. A reasonable agreement is obtained.Comment: 28 pages, LaTeX, 4 figure