Density Matrix Renormalisation Group Calculations for Two-Dimensional Lattices: An Application to the Spin-Half and Spin-One Square-Lattice Heisenberg Models

A new density matrix renormalisation group (DMRG) approach is presented for quantum systems of two spatial dimensions. In particular, it is shown that it is possible to create a multi-chain-type 2D DMRG approach which utilises previously determined system and environment blocks {\it at all points}. One firstly builds up effective quasi-1D system and environment blocks of width $L$ and these quasi-1D blocks are then used to as the initial building-blocks of a new 2D infinite-lattice algorithm. This algorithm is found to be competitive with those results of previous 2D DMRG algorithms and also of the best of other approximate methods. An illustration of this is given for the spin-half and spin-one Heisenberg models on the square lattice. The best results for the ground-state energies per bond of the spin-half and spin-one square-lattice Heisenberg antiferromagnets for the $N = 20 \times 20$ lattice using this treatment are given by $E_g/N_B = -0.3321$ and $E_g/N_B = -1.1525$, respectively.Comment: 7 Figures. Accepted for publication in Phys. Rev.

Local versus organic: a turn in consumer preferences and willingness-to-pay

Demand for local food in the United States has significantly increased over the last decade. In an attempt to understand the drivers of this demand and how they have changed over time, we investigate the literature on organic and local foods over the last few decades. We focus our review on studies that allow comparison of characteristics now associated with both local and organic food. We summarize the major findings of these studies and their implications for understanding drivers of local food demand. Prior to the late 1990s, most studies failed to consider factors now associated with local food, and the few that included these factors found very little support for them. In many cases, the lines between local and organic were blurred. Coincident with the development of federal organic food standards, studies began to find comparatively more support for local food as distinct and separate from organic food. Our review uncovers a distinct turn in the demand for local and organic food. Before the federal organic standards, organic food was linked to small farms, animal welfare, deep sustainability, community support, and many other factors that are not associated with most organic foods today. Based on our review, we argue that demand for local food arose largely in response to corporate cooptation of the organic food market and the arrival of “organic lite.” This important shift in consumer preferences away from organic and toward local food has broad implications for the environment and society. If these patterns of consumer preferences prove to be sustainable, producers, activists, and others should be aware of the implications that these trends have for the food system at large

Is J 133658.3-295105 a Radio Source at z >= 1.0 or at the Distance of M 83?

We present Gemini optical imaging and spectroscopy of the radio source J 133658.3-295105. This source has been suggested to be the core of an FR II radio source with two detected lobes. J 133658.3-295105 and its lobes are aligned with the optical nucleus of M 83 and with three other radio sources at the M 83 bulge outer region. These radio sources are neither supernova remnants nor H II regions. This curious configuration prompted us to try to determine the distance to J 133658.3-295105. We detected H_alpha emission redshifted by ~ 130 km s^-1 with respect to an M 83 H II region 2.5" east-southeast of the radio source. We do not detect other redshifted emission lines of an optical counterpart down to m_i = 22.2 +/- 0.8. Two different scenarios are proposed: the radio source is at z >= 2.5, a much larger distance than the previously proposed lower limit z >= 1.0, or the object was ejected by a gravitational recoil event from the M 83 nucleus. This nucleus is undergoing a strong dynamical evolution, judging from previous three-dimensional spectroscopy.Comment: 6 pages, 4 figure

Entanglement and symmetry in permutation symmetric states

We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We use the Majorana representation, where these states correspond to points on a sphere. Symmetry of the representation under rotation is equivalent to symmetry of the states under products of local unitaries. The geometric measure of entanglement is thus phrased entirely as a geometric optimisation, and a condition for the equivalence of entanglement measures written in terms of point symmetries. Finally we see that different symmetries of the states correspond to different types of entanglement with respect to SLOCC interconvertibility.Comment: 4 pages, 2 figures. Preliminary versions of some of these results were presented in the QIT 16 workshop in Japan, D. Markham, Proceedings of QIT 16, Japan (2007). Updated to reflect changes for publication: expanded proofs and some new examples give

Constraints on the radio loud/radio quiet dichotomy from the fundamental plane

The fundamental plane for black hole activity constitutes a tight correlation between jet power, X-ray luminosity, and black hole mass. Under the assumption that a Blandford-Znajek-type mechanism, which relies on black hole spin, contributes non-negligibly to jet production, the sufficiently small scatter in the fundamental plane shows that black hole spin differences of $\mid$$\Delta$a$\mid \sim$1 are not typical among the active galactic nuclei population. If $-$ as it seems $-$ radio loud and radio quiet objects are both faithful to the fundamental plane, models of black hole accretion in which the radio loud/radio quiet dichotomy is based on a spin dichotomy of a$\sim$1/a$\sim$0, respectively, are difficult to reconcile with the observations. We show how recent theoretical work based on differences in accretion flow orientation between retrograde and prograde, accommodates a small scatter in the fundamental plane for objects that do have non-negligible differences in black hole spin values. We also show that the dichotomy in spin between the most radio loud and the most radio quiet involves $\mid$$\Delta$a$\mid \approx$0. And, finally, we show how the picture that produces compatibility with the fundamental plane, also allows one to interpret other otherwise puzzling observations of jets across the mass scale including 1) the recently observed inverse relation between radio and X-rays at higher Eddington ratios in both black hole X-ray binaries as well as active galactic nuclei and 2) the apparent contradiction between jet power and black hole spin observed in X-ray hard and transitory burst states in X-ray binaries.Comment: 8 pages, 1 figure, accepted in MNRA

Bioeconomic Modeling of the Invasive Aquatic Plants Hydrilla verticillata (hydrilla), Eichhornia crassipes (water hyacinth), and Pistia stratiotes (water lettuce) and their impacts on angler effort on Florida lakes

The invasive aquatic plants Hydrilla verticillata (hydrilla), Eichhornia crassipes (water hyacinth), and Pistia stratiotes (water lettuce) have the potential to negatively impact recreational use of Florida lakes if consistent, adequate control expenditures are not made. In the mid-1990's, Florida significantly reduced its spending on invasive aquatic plant control measures, which resulted in a significant increase in needed control expenditures in subsequent years. This paper attempts to formalize a relationship between coverage of these invasive aquatic plants and angler effort on Florida lakes using data on 38 lakes over 20 years. Estimated regression coefficients are used to simulate control alternatives, and expenditure cost-benefit comparisons are made.Hydrilla, water hyacinth, water lettuce, bioeconomic, invasive, control, Resource /Energy Economics and Policy,

Evaluating the Potential for Technology Adoption in Mitigating Invasive Species Damage and Risk: Application to Zebra Mussels

Research and Development/Tech Change/Emerging Technologies, Resource /Energy Economics and Policy,