Monte Carlo Simulations of Quantum Spin Systems in the Valence Bond Basis

We discuss a projector Monte Carlo method for quantum spin models formulated in the valence bond basis, using the S=1/2 Heisenberg antiferromagnet as an example. Its singlet ground state can be projected out of an arbitrary basis state as the trial state, but a more rapid convergence can be obtained using a good variational state. As an alternative to first carrying out a time consuming variational Monte Carlo calculation, we show that a very good trial state can be generated in an iterative fashion in the course of the simulation itself. We also show how the properties of the valence bond basis enable calculations of quantities that are difficult to obtain with the standard basis of Sz eigenstates. In particular, we discuss quantities involving finite-momentum states in the triplet sector, such as the dispersion relation and the spectral weight of the lowest triplet.Comment: 15 pages, 7 figures, for the proceedings of "Computer Simulation Studies in Condensed Matter Physics XX

Pathways to Economic Mobility: Key Indicators

Outlines how indicators of social, human, and financial capital affect an individual's chances of moving up or down the economic ladder. Analyzes data on family structure, community, education, race/ethnicity, health, home ownership, and other factors

Flow of viscous fluid between slowly rotating, eccentric cylinders

The work of this thesis was undertaken to apply a method of analysis not previously applied to the problem of the slow flow of viscous fluid between two eccentric, rotating, infinitely long cylinders. This was accomplished under the assumption that both cylinders might be rotating and the entire general solution was retained. The stream function which was obtained has been expressed in terms of the original co-ordinates which had not been done previously;In chapter IV is obtained the torque and thrust on a cylinder. The difference between the torques on the cylinders was found to be proportional to the eccentricity, which result agrees with the result obtained by D. L. Holl. The limiting value of the torque as the cylinders became concentric was also obtained and is in agreement with results obtained by others;Special cases of the flow between eccentric cylinders, extending those discussed by Muller, are presented in section 9. These bring out more vividly the effect of changing eccentricity and the effect of changing the relative velocities of the two cylinders;The problems: in the theory of thin plates which corresponds to this hydrodynamic problem is discussed in section 10

Master equation approach to computing RVB bond amplitudes

We describe a "master equation" analysis for the bond amplitudes h(r) of an RVB wavefunction. Starting from any initial guess, h(r) evolves (in a manner dictated by the spin hamiltonian under consideration) toward a steady-state distribution representing an approximation to the true ground state. Unknown transition coefficients in the master equation are treated as variational parameters. We illustrate the method by applying it to the J1-J2 antiferromagnetic Heisenberg model. Without frustration (J2=0), the amplitudes are radially symmetric and fall off as 1/r^3 in the bond length. As the frustration increases, there are precursor signs of columnar or plaquette VBS order: the bonds preferentially align along the axes of the square lattice and weight accrues in the nearest-neighbour bond amplitudes. The Marshall sign rule holds over a large range of couplings, J2/J1 < 0.418. It fails when the r=(2,1) bond amplitude first goes negative, a point also marked by a cusp in the ground state energy. A nonrigourous extrapolation of the staggered magnetic moment (through this point of nonanalyticity) shows it vanishing continuously at a critical value J2/J1 = 0.447. This may be preempted by a first-order transition to a state of broken translational symmetry.Comment: 8 pages, 7 figure

Crop Monitoring in Australia Using Digital Analysis of Landsat Data

This paper describes on-going co-operative research by the New South Wales (N.S.W.) Department of Agriculture and IBM Australia Limited. The aims of the project are to investigate if Landsat digital data can be used to map and monitor agricultural resources, particularly crop acreages and production, over large areas. From the outset, multi-temporal whole scene computation has been a feature of the technical approach. Software modifications for large data volumes were carried out allowing supervised maximum likelihood classification to be used throughout the work. Considerable amounts of agronomic ground truth have been collected over wide latitudes for use in training the computer system as well as for accuracy assessment of classification results. A number of Landsat scenes have been studied, with three to five acquisitions being registered for each. Preliminary analyses were conducted on historical data of Tamworth (N.S.W.) and Narrabri (N.S.W.) scenes. More intensive studies were undertaken for the 1980-81 wheat season in the Narrabri scene and are currently being undertaken in the Horsham (Victoria) scene. The techniques used and results from these analyses are discussed in this paper. Classification accuracy has been very encouraging showing excellent potential for use in crop area and production estimates. Various problems emerged which required special attention and these are discussed. They included loss of data because of cloud cover, registration accuracy, training techniques, best combinations of bands and dates for classification, confusion classes, computation of very large volumes of data and classification accuracy assessment. This work is demonstrating valuable applications of Landsat data in Australia. Technology transfer to other users is under way and it is anticipated that further technological development will lead to large scale adoption of remote sensing techniques for monitoring agricultural resources in Australia

An Application of Large Scale Computing Facilities to the Processing of LANDSAT Digital Data in Australia

An early issue in the Australian Wide Scale Wheat Monitoring Project, started in November, 1978, was whether to use area sampling, as in the LACIE, or to be innovative and attempt whole scene processing. The availability of a large computing system and acknowledgment of the trends in price and performance of computers influenced a decision towards whole scene processing. The computing facilities used in this project are described. An interactive facility supported by software called ER-MAN II is installed on an IBM 3033 which simultaneously supports several hundred other interactive users. The pros and cons of using such a shared facility for this type of work are explored. The use of multi-temporal data has been the essence of the approach in this project. Reasons for its use, and its performance implications are discussed from the computing view point. Results to date indicate that shared use of a large facility is feasible and effective. In addition, some calculations may not be possible on small CPU\u27s. While the interactive processing of the combination of multi-temporal LANDSAT data and large areas is not common in Australia now, it is probable that its use will increase as the cost of computing equipment decreases