Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators

The integrable quantum models, associated to the transfer matrices of the 6-vertex reflection algebra for spin 1/2 representations, are studied in this paper. In the framework of Sklyanin's quantum separation of variables (SOV), we provide the complete characterization of the eigenvalues and eigenstates of the transfer matrix and the proof of the simplicity of the transfer matrix spectrum. Moreover, we use these integrable quantum models as further key examples for which to develop a method in the SOV framework to compute matrix elements of local operators. This method has been introduced first in [1] and then used also in [2], it is based on the resolution of the quantum inverse problem (i.e. the reconstruction of all local operators in terms of the quantum separate variables) plus the computation of the action of separate covectors on separate vectors. In particular, for these integrable quantum models, which in the homogeneous limit reproduce the open spin-1/2 XXZ quantum chains with non-diagonal boundary conditions, we have obtained the SOV-reconstructions for a class of quasi-local operators and determinant formulae for the covector-vector actions. As consequence of these findings we provide one determinant formulae for the matrix elements of this class of reconstructed quasi-local operators on transfer matrix eigenstates.Comment: 40 pages. Minor modifications in the text and some notations and some more reference adde

Potential pesticide transport in Colorado agriculture: a model comparison

.30 September 1989.Includes bibliographical references (pages [50]-52)Grant no. 14-08-0001-1551, Project no. 09; financed in part by the U.S. Department of the Interior, Geological Survey, through the Colorado Water Resources Research Institute

C9orf72 repeat expansions cause neurodegeneration in Drosophila through arginine-rich proteins

An expanded GGGGCC repeat in C9orf72 is the most common genetic cause of frontotemporal dementia and amyotrophic lateral sclerosis. A fundamental question is whether toxicity is driven by the repeat RNA itself and/or by dipeptide repeat proteins generated by repeat-associated, non-ATG translation. To address this question we developed in vitro and in vivo models to dissect repeat RNA and dipeptide repeat protein toxicity. Expression of pure repeats in Drosophila caused adult-onset neurodegeneration attributable to poly-(glycine-arginine) proteins. Thus, expanded repeats promoted neurodegeneration through neurotoxic proteins. Expression of individual dipeptide repeat proteins with a non-GGGGCC RNA sequence showed both poly-(glycine-arginine) and poly-(proline-arginine) proteins caused neurodegeneration. These findings are consistent with a dual toxicity mechanism, whereby both arginine-rich proteins and repeat RNA contribute to C9orf72-mediated neurodegeneration

Point-like topological defects in bilayer quantum Hall systems

Following a suggestion given in Phys. Lett. B 571 (2003) 250, we show how a bilayer Quantum Hall system at fillings nu =m/pm+2 can exhibit a point-like topological defect in its edge state structure. Indeed our CFT theory for such a system, the Twisted Model (TM), gives rise in a natural way to such a feature in the twisted sector. Our results are in agreement with recent experimental findings (cond-mat/0503478) which evidence the presence of a topological defect in the bilayer system.Comment: 9 pages, 3 figure

Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model

The spin-1/2 highest weight representations of the dynamical 6-vertex and the standard 8-vertex Yang-Baxter algebra on a finite chain are considered in this paper. For the antiperiodic dynamical 6-vertex transfer matrix defined on chains with an odd number of sites, we adapt the Sklyanin's quantum separation of variable (SOV) method and explicitly construct SOV representations from the original space of representations. We provide the complete characterization of eigenvalues and eigenstates proving also the simplicity of its spectrum. Moreover, we characterize the matrix elements of the identity on separated states by determinant formulae. The matrices entering in these determinants have elements given by sums over the SOV spectrum of the product of the coefficients of separate states. This SOV analysis is not reduced to the case of the elliptic roots of unit and the results here derived define the required setup to extend to the dynamical 6-vertex model the approach recently developed in [1]-[5] to compute the form factors of the local operators in the SOV framework, these results will be presented in a future publication. For the periodic 8-vertex transfer matrix, we prove that its eigenvalues have to satisfy a fixed system of equations. In the case of a chain with an odd number of sites, this system of equations is the same entering in the SOV characterization of the antiperiodic dynamical 6-vertex transfer matrix spectrum. This implies that the set of the periodic 8-vertex eigenvalues is contained in the set of the antiperiodic dynamical 6-vertex eigenvalues. A criterion is introduced to find simultaneous eigenvalues of these two transfer matrices and associate to any of such eigenvalues one nonzero eigenstate of the periodic 8-vertex transfer matrix by using the SOV results. Moreover, a preliminary discussion on the degeneracy of the periodic 8-vertex spectrum is also presented.Comment: 36 pages, main modifications in section 3 and one appendix added, no result modified for the dynamical 6-vertex transfer matrix spectrum and the matrix elements of identity on separate states for chains with an odd number of site

Topological order in Josephson junction ladders with Mobius boundary conditions

We propose a CFT description for a closed one-dimensional fully frustrated ladder of quantum Josephson junctions with Mobius boundary conditions, in particular we show how such a system can develop topological order. Such a property is crucial for its implementation as a "protected" solid state qubit.Comment: 14 pages, 3 figures, to appear in JSTA

Mixed-Species Plantation Effects on Soil Biological and Chemical Quality and Tree Growth of a Former Agricultural Land

Tree planting on abandoned agricultural land could both restore the soil quality and increase the productivity of economically valuable woody species. Here, we assess the impact of mixed-species tree plantations on soil quality at a site in Central Italy where tree intercropping systems were established 20 years ago on a former agricultural land. These intercropping systems include two species of economic interest, Populus alba and Juglans regia, and one of three different nurse trees, i.e., Alnus cordata, Elaeagnus umbellata, both of which are N-fixing species, and Corylus avellana. We measured tree growth and compared how soil organic matter, soil extracellular enzymes, and nematodes of different feeding groups varied among the intercropping systems and relative to a conventional agricultural field. Our results indicate that tree plantation led to an increase in soil carbon and nitrogen, and enhanced enzyme activities, compared with the agricultural land. The proportion of nematode feeding groups was heterogeneous, but predators were absent from the agricultural soil. Multivariate analysis of soil properties, enzymatic activity, nematodes, and tree growth point to the importance of the presence N-fixing species, as the presence of A. cordata was linked to higher soil quality, and E. umbellata to growth of the associated valuable woody species. Our findings indicate that intercropping tree species provide a tool for both restoring fertility and improving soil quality