Ab Initio Calculations of the Spin-Half XY Model

In this article, the correlated basis-function (CBF) method is applied for the first time to the quantum spin-half {\it XY} model on the linear chain, the square lattice, and the simple cubic lattice. In this treatment of the quantum spin-half {\it XY} model a Jastrow ansatz is utilised to approximate the ground-state wave function. Results for the ground-state energy and the sublattice magnetisation are presented, and evidence that the CBF detects the quantum phase transition point in this model is also presented. The CBF results are compared to previous coupled cluster method (CCM) results for the spin-half {\it XY} model, and the two formalisms are then compared and contrasted.Comment: 10 pages, 3 figure

Sure to rise: reading the Edmonds cookery book as a popular icon

Cookbooks are one of a variety of written forms that can be read as historical documents, functioning as testaments to individual, familial and cultural development. In the recipe, one can find a sense of culinary preference which simultaneously shapes and is shaped by a sense of belonging and identity. The (post-) colonial past of countries such as New Zealand and Australia allows a particular view into reading cookery books as chronicles of everyday life as well as an archive of cultural memory, uses and popular customs. Starting from the premise that cookbooks can function as a site for heritage and identity, this paper addresses the status of the Edmonds cookery kook as a popularised national icon. Now an established presence within New Zealand’s culinary culture, the Edmonds collection – first published in 1908 as The sure to rise cookery book – has evolved over the decades to include new and updated recipes, mirroring the cultural and socio-historical moment in which it was placed. With this in mind, I analyse how cookbook writing can be interpreted as a national practice which owes a lot of its success to pervasive links to popular culture. My paper also offers a critical framework which highlights the material conditions – historical, aesthetico-political and socio-cultural – that encouraged the rise and popularity of the Edmonds cookbook within an expanding national readership

St Aidan's College, Grahamstown: a history

by Francis L. Coleman ; with two chapters by Tony FarnellIncludes bibliographical reference

Ab Initio Treatments of the Ising Model in a Transverse Field

In this article, new results are presented for the zero-temperature ground-state properties of the spin-half transverse Ising model on various lattices using three different approximate techniques. These are, respectively, the coupled cluster method, the correlated basis function method, and the variational quantum Monte Carlo method. The methods, at different levels of approximation, are used to study the ground-state properties of these systems, and the results are found to be in excellent agreement both with each other and with results of exact calculations for the linear chain and results of exact cumulant series expansions for lattices of higher spatial dimension. The different techniques used are compared and contrasted in the light of these results, and the constructions of the approximate ground-state wave functions are especially discussed.Comment: 28 Pages, 4 Figures, 1 Tabl

Synaptic transmission at visualized sympathetic boutons: stochastic interaction between acetylcholine and its receptors

Excitatory postsynaptic currents (EPSCs) were recorded with loose patch electrodes placed over visualized boutons on the surface of rat pelvic ganglion cells. At 34 degrees C the time to peak of the EPSC was about 0.7 ms, and a single exponential described the declining phase with a time constant of about 4.0 ms; these times were not correlated with changes in the amplitude of the EPSC. The amplitude-frequency histogram of the EPSC at individual boutons was well described by a single Gaussian-distribution that possessed a variance similar to that of the electrical noise. Nonstationary fluctuation analysis of the EPSCs at a bouton indicated that about 120 ACh receptor channels were available beneath boutons for interaction with a quantum of ACh. The characteristics of these EPSCs were compared with the results of Monte Carlo simulations of the quantal release of 9000 acetylcholine (ACh) molecules onto receptor patches of density 1400 microns-2 and 0.41 micron diameter, using a kinetic scheme of interaction between ACh and the receptors similar to that observed at the neuromuscular junction. The simulated EPSC generated in this way had temporal characteristics similar to those of the experimental EPSC when either the diffusion of the ACh is slowed or allowance is made for a finite period of transmitter release from the bouton. The amplitude of the simulated EPSC then exhibited stochastic fluctuations similar to those of the experimental EPSC

High-Order Coupled Cluster Method Calculations for the Ground- and Excited-State Properties of the Spin-Half XXZ Model

In this article, we present new results of high-order coupled cluster method (CCM) calculations, based on a N\'eel model state with spins aligned in the $z$-direction, for both the ground- and excited-state properties of the spin-half {\it XXZ} model on the linear chain, the square lattice, and the simple cubic lattice. In particular, the high-order CCM formalism is extended to treat the excited states of lattice quantum spin systems for the first time. Completely new results for the excitation energy gap of the spin-half {\it XXZ} model for these lattices are thus determined. These high-order calculations are based on a localised approximation scheme called the LSUB$m$ scheme in which we retain all $k$-body correlations defined on all possible locales of $m$ adjacent lattice sites ($k \le m$). The ``raw'' CCM LSUB$m$ results are seen to provide very good results for the ground-state energy, sublattice magnetisation, and the value of the lowest-lying excitation energy for each of these systems. However, in order to obtain even better results, two types of extrapolation scheme of the LSUB$m$ results to the limit $m \to \infty$ (i.e., the exact solution in the thermodynamic limit) are presented. The extrapolated results provide extremely accurate results for the ground- and excited-state properties of these systems across a wide range of values of the anisotropy parameter.Comment: 31 Pages, 5 Figure

Non-Invasive Hall Current Distribution Measurement in a Hall Effect Thruster

A means is presented to determine the Hall current density distribution in a closed drift thruster by remotely measuring the magnetic field and solving the inverse problem for the current density. The magnetic field was measured by employing an array of eight tunneling magnetoresistive (TMR) sensors capable of milligauss sensitivity when placed in a high background field. The array was positioned just outside the thruster channel on a 1.5 kW Hall thruster equipped with a center-mounted hollow cathode. In the sensor array location, the static magnetic field is approximately 30 G, which is within the linear operating range of the TMR sensors. Furthermore, the induced field at this distance is approximately tens of milligauss, which is within the sensitivity range of the TMR sensors. Because of the nature of the inverse problem, the induced-field measurements do not provide the Hall current density by a simple inversion; however, a Tikhonov regularization of the induced field does provide the current density distributions. These distributions are shown as a function of time in contour plots. The measured ratios between the average Hall current and the average discharge current ranged from 6.1 to 7.3 over a range of operating conditions from 1.3 kW to 2.2 kW. The temporal inverse solution at 1.5 kW exhibited a breathing mode frequency of 24 kHz, which was in agreement with temporal measurements of the discharge current

Magnetic phases of the mixed-spin J1−J2J_1-J_2 Heisenberg model on a square lattice

We study the zero-temperature phase diagram and the low-energy excitations of a mixed-spin ($S_1>S_2$) $J_1-J_2$ Heisenberg model defined on a square lattice by using a spin-wave analysis, the coupled cluster method, and the Lanczos exact-diagonalization technique. As a function of the frustration parameter $J_2/J_1$ ($>0$), the phase diagram exhibits a quantized ferrimagnetic phase, a canted spin phase, and a mixed-spin collinear phase. The presented results point towards a strong disordering effect of the frustration and quantum spin fluctuations in the vicinity of the classical spin-flop transition. In the extreme quantum system $(S_1,S_2)=(1,{1/2})$, we find indications of a new quantum spin state in the region $0.46< J_2/J_1<0.5$Comment: 5 PRB pages, 7 figure

A Recursive Method of the Stochastic State Selection for Quantum Spin Systems

In this paper we propose the recursive stochastic state selection method, an extension of the recently developed stochastic state selection method in Monte Carlo calculations for quantum spin systems. In this recursive method we use intermediate states to define probability functions for stochastic state selections. Then we can diminish variances of samplings when we calculate expectation values of the powers of the Hamiltonian. In order to show the improvement we perform numerical calculations of the spin-1/2 anti-ferromagnetic Heisenberg model on the triangular lattice. Examining results on the ground state of the 21-site system we confide this method in its effectiveness. We also calculate the lowest and the excited energy eigenvalues as well as the static structure factor for the 36-site system. The maximum number of basis states kept in a computer memory for this system is about 3.6 x 10**7. Employing a translationally invariant initial trial state, we evaluate the lowest energy eigenvalue within 0.5 % of the statistical errors.Comment: 14 pages, 1 figur