Matrix Product States: Symmetries and Two-Body Hamiltonians

We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple tensor. We exploit this result in order to prove and extend a version of the Lieb-Schultz-Mattis theorem, one of the basic results in many-body physics, in the context of MPS. We illustrate the results with an exhaustive search of SU(2)--invariant two-body Hamiltonians which have such MPS as exact ground states or excitations.Comment: PDFLatex, 12 pages and 6 figure

Compressibility and structural stability of ultra-incompressible bimetallic interstitial carbides and nitrides

We have investigated by means of high-pressure x-ray diffraction the structural stability of Pd2Mo3N, Ni2Mo3C0.52N0.48, Co3Mo3C0.62N0.38, and Fe3Mo3C. We have found that they remain stable in their ambient-pressure cubic phase at least up to 48 GPa. All of them have a bulk modulus larger than 330 GPa, being the least compressible material Fe3Mo3C, B0 = 374(3) GPa. In addition, apparently a reduction of compressibility is detected as the carbon content increased. The equation of state for each material is determined. A comparison with other refractory materials indicates that interstitial nitrides and carbides behave as ultra-incompressible materials.Comment: 14 pages, 3 figures, 1 tabl

Rubidium and zirconium abundances in massive Galactic asymptotic giant branch stars revisited

Luminous Galactic OH/IR stars have been identified as massive (>4-5 M_s) AGB stars experiencing HBB and Li production. Their Rb abundances and [Rb/Zr] ratios derived from hydrostatic model atmospheres, are significantly higher than predictions from AGB nucleosynthesis models, posing a problem to our understanding of AGB evolution and nucleosynthesis. We report new Rb and Zr abundances in the full sample of massive Galactic AGB stars, previously studied with hydrostatic models, by using more realistic extended model atmospheres. We use a modified version of the spectral synthesis code Turbospectrum and consider the presence of a circumstellar envelope and radial wind. The Rb and Zr abundances are determined from the 7800 A Rb I resonant line and the 6474 A ZrO bandhead, respectively, and we explore the sensitivity of the derived abundances to variations of the stellar (Teff) and wind (M_loss, beta and vexp) parameters in the extended models. The Rb and Zr abundances derived from the best spectral fits are compared with the most recent AGB nucleosynthesis theoretical models. The new Rb abundances are much lower (even 1-2 dex) than those derived with the hydrostatic models, while the Zr abundances are similar. The Rb I line profile and Rb abundance are very sensitive to the M_loss rate but much less sensitive to variations of the wind velocity-law and the vexp(OH). We confirm the earlier preliminary results based on a smaller sample of massive O-rich AGB stars, that the use of extended atmosphere models can solve the discrepancy between the AGB nucleosynthesis theoretical models and the observations of Galactic massive AGB stars. The Rb abundances, however, are still strongly dependent of the M_loss, which is unknown in these AGB stars. Accurate M_loss rates in these massive Galactic AGB stars are needed in order to break the models degeneracy and get reliable Rb abundances in these stars.Comment: Accepted for publication in A&A, 14 pages, 12 figures, 4 table

Estimating causal networks in biosphere–atmosphere interaction with the PCMCI approach

Local meteorological conditions and biospheric activity are tightly coupled. Understanding these links is an essential prerequisite for predicting the Earth system under climate change conditions. However, many empirical studies on the interaction between the biosphere and the atmosphere are based on correlative approaches that are not able to deduce causal paths, and only very few studies apply causal discovery methods. Here, we use a recently proposed causal graph discovery algorithm, which aims to reconstruct the causal dependency structure underlying a set of time series. We explore the potential of this method to infer temporal dependencies in biosphere-atmosphere interactions. Specifically we address the following questions: How do periodicity and heteroscedasticity influence causal detection rates, i.e. the detection of existing and non-existing links? How consistent are results for noise-contaminated data? Do results exhibit an increased information content that justifies the use of this causal-inference method? We explore the first question using artificial time series with well known dependencies that mimic real-world biosphere-atmosphere interactions. The two remaining questions are addressed jointly in two case studies utilizing observational data. Firstly, we analyse three replicated eddy covariance datasets from a Mediterranean ecosystem at half hourly time resolution allowing us to understand the impact of measurement uncertainties. Secondly, we analyse global NDVI time series (GIMMS 3g) along with gridded climate data to study large-scale climatic drivers of vegetation greenness. Overall, the results confirm the capacity of the causal discovery method to extract time-lagged linear dependencies under realistic settings. The violation of the method's assumptions increases the likelihood to detect false links. Nevertheless, we consistently identify interaction patterns in observational data. Our findings suggest that estimating a directed biosphere-atmosphere network at the ecosystem level can offer novel possibilities to unravel complex multi-directional interactions. Other than classical correlative approaches, our findings are constrained to a few meaningful set of relations which can be powerful insights for the evaluation of terrestrial ecosystem models

Evaluation of kraft cooking behaviour for different hardwood species

In this study six wood species (birch, chestnut, oak, beech, poplar and eucalyptus) were analysed separately. Lignin content, Polysaccharides content (cellulose and hemicelluloses), Yield, Hexenuronic acids were evaluated for three cooking temperatures (140ºC, 150ºC and 160ºC) and different cooking times. Common cooking conditions were applied and temperature program included cold impregnation, a plateau at 110°C (2.5 hours) to perform initial delignification separately followed by a second plateau at cooking temperature. The results of PCA show that the almost all parameters (excluding hexenuronic acids) are well correlated between them (total variance: 62%). For Eucalyptus and poplar species the hemicelluloses content aren’t well correlated with the previously parameter, caused by the difference observed for the higher temperatures. In some samples was observed that xylans are partially resistant and their elimination is only partial (30 to 40%) in the early stage of cooking. For the highest cooking time there were observed a significant difference between the three temperatures studied. Chestnut and oak wood species present a different behaviour compared with the other species, caused by their similar anatomical and chemical structure. For the 160º of cooking temperature in the second plateau was the poplar, beech and birch that present a different performance

Perturbations with angular momentum of Robinson-Trautman spacetimes

We study the possible asymptotically flat perturbations of Robinson-Trautman spacetimes. We differentiate between algebraically special perturbations and general perturbations. The equations that determine physically realistic spacetimes with angular momentum are presented.Comment: 23 pages, no figure