Angular Momentum Distribution Function of the Laughlin Droplet

We have evaluated the angular-momentum distribution functions for finite numbers of electrons in Laughlin states. For very small numbers of electrons the angular-momentum state occupation numbers have been evaluated exactly while for larger numbers of electrons they have been obtained from Monte-Carlo estimates of the one-particle density matrix. An exact relationship, valid for any number of electrons, has been derived for the ratio of the occupation numbers of the two outermost orbitals of the Laughlin droplet and is used to test the accuracy of the MC calculations. We compare the occupation numbers near the outer edges of the droplets with predictions based on the chiral Luttinger liquid picture of Laughlin state edges and discuss the surprisingly large oscillations in occupation numbers which occur for angular momenta far from the edge.Comment: 11 pages of RevTeX, 2 figures available on request. IUCM93-00

Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics

We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function factorizes in the form characteristic of an ideal gas. The virial expansion is exactly computable and interestingly it is only the second virial coefficient that encodes the statistics information.Comment: 10pp, REVTE

Some Properties of the Calogero-Sutherland Model with Reflections

We prove that the Calogero-Sutherland Model with reflections (the BC_N model) possesses a property of duality relating the eigenfunctions of two Hamiltonians with different coupling constants. We obtain a generating function for their polynomial eigenfunctions, the generalized Jacobi polynomials. The symmetry of the wave-functions for certain particular cases (associated to the root systems of the classical Lie groups B_N, C_N and D_N) is also discussed.Comment: 16 pages, harvmac.te

Long Range Interaction Models and Yangian Symmetry

The generalized Sutherland-Romer models and Yan models with internal spin degrees are formulated in terms of the Polychronakos' approach and RTT relation associated to the Yang-Baxter equation in consistent way. The Yangian symmetry is shown to generate both models. We finally introduce the reflection algebra K(u) to the long range models.Comment: 13 pages, preprint of Nankai Institute of Mathematics ( Theoretical Physics Division ), published in Physical Review E of 1995. For hard copy, write to Prof. Mo-lin GE directly. Do not send emails to this accoun

\u27Dermo\u27 fleece rot and body strike on sheep

Blowfly strike is one of the major problems confronting the sheep industry in Austrsalia, with an estimated totsalcost of control eceeding $100 million each year. Sheep are susceptible to five types of strike: body, breach, poll, pizzle and wound. Body strike, is of greater economic importance because its sporadic occurence from year to year makes it difficult to predict and cintrol. Outbreaks of body strike after rain can affect large numbers of sheep and inflict severe production losses. In eastern Australia fleece rot is generally considered to be the main predisposing factor to blowfly strike, but in Western Australia evidence suggests that dermatophilosis - or \u27dermo\u27 - is the more important factor

Novel classical ground state of a many body system in arbitrary dimensions

The classical ground state of a D- dimensional many body system with two and three body interactions is studied as a function of the strength of the three body interaction. We prove exactly that beyond a critical strength of the three body interaction, the classical ground state of the system is one in which all the particles are on a line. The positions of the particles in this string configuration are uniquely determined by the zeros of the Hermite polynomials.Comment: 4 pages, RevTeX, no figure; version to appear in Physical Review Letter

Electron Addition Spectrum in the Supersymmetric t-J Model with Inverse-Square Interaction

The electron addition spectrum A^+(k,omega) is obtained analytically for the one-dimensional (1D) supersymmetric t-J model with 1/r^2 interaction. The result is obtained first for a small-sized system and its validity is checked against the numerical calculation. Then the general expression is found which is valid for arbitrary size of the system. The thermodynamic limit of A^+(k,omega) has a simple analytic form with contributions from one spinon, one holon and one antiholon all of which obey fractional statistics. The upper edge of A^+(k,omega) in the (k,omega) plane includes a delta-function peak which reduces to that of the single-electron band in the low-density limit.Comment: 5 pages, 1 figure, accepted for publication in Phys. Rev. Let

Planar N=4 Gauge Theory and the Hubbard Model

Recently it was established that a certain integrable long-range spin chain describes the dilatation operator of N=4 gauge theory in the su(2) sector to at least three-loop order, while exhibiting BMN scaling to all orders in perturbation theory. Here we identify this spin chain as an approximation to an integrable short-ranged model of strongly correlated electrons: The Hubbard model.Comment: 35 pages, 2 figures; v2: typos and references fixed, published versio

Interactions of a Light Hypersonic Jet with a Non-Uniform Interstellar Medium

We present three dimensional simulations of the interaction of a light hypersonic jet with an inhomogeneous thermal and turbulently supported disk in an elliptical galaxy. We model the jet as a light, supersonic non-relativistic flow with parameters selected to be consistent with a relativistic jet with kinetic power just above the FR1/FR2 break. We identify four generic phases in the evolution of such a jet with the inhomogeneous interstellar medium: 1) an initial ``flood and channel'' phase, where progress is characterized by high pressure gas finding changing weak points in the ISM, flowing through channels that form and re-form over time, 2) a spherical, energy-driven bubble phase, were the bubble is larger than the disk scale, but the jet remains fully disrupted close to the nucleus, 3) a rapid, jet break--out phase the where jet breaks free of the last dense clouds, becomes collimated and pierces the spherical bubble, and 4) a classical phase, the jet propagates in a momentum-dominated fashion leading to the classical jet + cocoon + bow-shock structure. Mass transport in the simulations is investigated, and we propose a model for the morphology and component proper motions in the well-studied Compact Symmetric Object 4C31.04.Comment: 66 pages, 22 figures, PDFLaTeX, aastex macros, graphicx and amssymb packages, Accepted, to be published 2007 ApJ