Algorithms to solve the Sutherland model

We give a self-contained presentation and comparison of two different algorithms to explicitly solve quantum many body models of indistinguishable particles moving on a circle and interacting with two-body potentials of $1/\sin^2$-type. The first algorithm is due to Sutherland and well-known; the second one is a limiting case of a novel algorithm to solve the elliptic generalization of the Sutherland model. These two algorithms are different in several details. We show that they are equivalent, i.e., they yield the same solution and are equally simple.Comment: 15 pages, LaTe

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

Genomic regions associated with common root rot resistance in the barley variety Delta

Common root rot (CRR) caused by Bipolaris sorokiniana is a serious disease constraint in the dry temperate cereal growing regions of the world. Currently little is known about the genetic control of resistance to CRR in cereals. In this study based on a Delta/Lindwall barley population we have undertaken a bulked segregant analysis (BSA) and whole genome mapping approach utilising Diversity Arrays Technology (DArT) to identified quantitative trait loci (QTL) associated with CRR expression. One QTL each was identified on chromosomes 4HL and 5HL explaining 12 and 11% of the phenotypic variance, respectively

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

Transport Properties of a One-Dimensional Two-Component Quantum Liquid with Hyperbolic Interactions

We present an investigation of the sinh-cosh (SC) interaction model with twisted boundary conditions. We argue that, when unlike particles repel, the SC model may be usefully viewed as a Heisenberg-Ising fluid with moving Heisenberg-Ising spins. We derive the Luttinger liquid relation for the stiffness and the susceptibility, both from conformal arguments, and directly from the integral equations. Finally, we investigate the opening and closing of the ground state gaps for both SC and Heisenberg-Ising models, as the interaction strength is varied.Comment: 10 REVTeX pages + 4 uuencoded figures, UoU-002029

Density Correlation Functions in Calogero Sutherland Models

Using arguments from two dimensional Yang-Mills theory and the collective coordinate formulation of the Calogero-Sutherland model, we conjecture the dynamical density correlation function for coupling $l$ and $1/l$, where $l$ is an integer. We present overwhelming evidence that the conjecture is indeed correct.Comment: 12 pages phyzzx, CERN-TH/94.7243 One reference change

The lifecycle of axisymmetric internal solitary waves

The generation and evolution of solitary waves by intrusive gravity currents in an approximate two-layer fluid with equal upper- and lower-layer depths is examined in a cylindrical geometry by way of theory and numerical simulations. The study is limited to vertically symmetric cases in which the density of the intruding fluid is equal to the average density of the ambient. We show that even though the head height of the intrusion decreases, it propagates at a constant speed well beyond 3 lock radii. This is because the strong stratification at the interface supports the formation of a mode-2 solitary wave that surrounds the intrusion head and carries it outwards at a constant speed. The wave and intrusion propagate faster than a linear long wave; therefore, there is strong supporting evidence that the wave is indeed nonlinear. Rectilinear Korteweg-de Vries theory is extended to allow the wave amplitude to decay as <i>r<sup>-p</sup></I> with <i>p</i>=½ and the theory is compared to the observed waves to demonstrate that the width of the wave scales with its amplitude. After propagating beyond 7 lock radii the intrusion runs out of fluid. Thereafter, the wave continues to spread radially at a constant speed, however, the amplitude decreases sufficiently so that linear dispersion dominates and the amplitude decays with distance as <i>r</i><sup>-1</sup>

Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons

We calculate the exact dynamical magnetic structure factor S(Q,E) in the ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2 spinon excitations, the Haldane-Shastry model with inverse-square exchange, which is in the same low-energy universality class as Bethe's nearest-neighbor exchange model. Only two-spinon excited states contribute, and S(Q,E) is found to be a very simple integral over these states.Comment: 11 pages, LaTeX, RevTeX 3.0, cond-mat/930903

Effect of Intermolecular Interactions between CH Frequencies on the Infrared Spectra of N‐Paraffins and Polythene

A systematic study has been made of the infrared absorption band near 725 cm—1 which arises from the rocking vibration of methylene groups in n‐paraffins and in polyethylene. In unoriented crystals of n‐paraffins, this band exhibits two components of equal intensity below the transition point; above the transition temperature and in the liquid state only the higher frequency component is found. In solid cold‐drawn polyethylene the two components are of unequal intensity, the low frequency component being the stronger; in liquid polyethylene only the lower frequency component is found. Studies were made of polyethylene in various states of crystallinity and orientation, using both polarized and unpolarized radiation. The results obtained can be consistently interpreted, if the higher frequency component is attributed to crystallites in the polyethylene and the lower frequency component is assumed to be due partly to the crystalline and partly to the amorphous form of the polyethylene. It is concluded that the doubling of this frequency arises from some interaction between methylene groups which is peculiar to the crystalline state of long chain n‐paraffins below their transition points.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69988/2/JCPSA6-22-12-1993-1.pd

The Dynamics of the One-Dimensional Delta-Function Bose Gas

We give a method to solve the time-dependent Schroedinger equation for a system of one-dimensional bosons interacting via a repulsive delta function potential. The method uses the ideas of Bethe Ansatz but does not use the spectral theory of the associated Hamiltonian