Entanglement from density measurements: analytical density-functional for the entanglement of strongly correlated fermions

We derive an analytical density functional for the single-site entanglement of the one-dimensional homogeneous Hubbard model, by means of an approximation to the linear entropy. We show that this very simple density functional reproduces quantitatively the exact results. We then use this functional as input for a local density approximation to the single-site entanglement of inhomogeneous systems. We illustrate the power of this approach in a harmonically confined system, which could simulate recent experiments with ultracold atoms in optical lattices as well as in a superlattice and in an impurity system. The impressive quantitative agreement with numerical calculations -- which includes reproducing subtle signatures of the particle density stages -- shows that our density-functional can provide entanglement calculations for actual experiments via density measurements. Next we use our functional to calculate the entanglement in disordered systems. We find that, at contrast with the expectation that disorder destroys the entanglement, there exist regimes for which the entanglement remains almost unaffected by the presence of disordered impurities.Comment: 6 pages, 3 figure

Feasibility of approximating spatial and local entanglement in long-range interacting systems using the extended Hubbard model

We investigate the extended Hubbard model as an approximation to the local and spatial entanglement of a one-dimensional chain of nanostructures where the particles interact via a long range interaction represented by a `soft' Coulomb potential. In the process we design a protocol to calculate the particle-particle spatial entanglement for the Hubbard model and show that, in striking contrast with the loss of spatial degrees of freedom, the predictions are reasonably accurate. We also compare results for the local entanglement with previous results found using a contact interaction (PRA, 81 (2010) 052321) and show that while the extended Hubbard model recovers a better agreement with the entanglement of a long-range interacting system, there remain realistic parameter regions where it fails to predict the quantitative and qualitative behaviour of the entanglement in the nanostructure system.Comment: 6 pages, 5 figures and 1 table; added results with correlated hopping term; accepted by EP

Hubbard model as an approximation to the entanglement in nanostructures

We investigate how well the one-dimensional Hubbard model describes the entanglement of particles trapped in a string of quantum wells. We calculate the average single-site entanglement for two particles interacting via a contact interaction and consider the effect of varying the interaction strength and the interwell distance. We compare the results with the ones obtained within the one-dimensional Hubbard model with on-site interaction. We suggest an upper bound for the average single-site entanglement for two electrons in M wells and discuss analytical limits for very large repulsive and attractive interactions. We investigate how the interplay between interaction and potential shape in the quantum-well system dictates the position and size of the entanglement maxima and the agreement with the theoretical limits. Finally, we calculate the spatial entanglement for the quantum-well system and compare it to its average single-site entanglement

Effect of spatial inhomogeneity on the mapping between strongly interacting fermions and weakly interacting spins

A combined analytical and numerical study is performed of the mapping between strongly interacting fermions and weakly interacting spins, in the framework of the Hubbard, t-J and Heisenberg models. While for spatially homogeneous models in the thermodynamic limit the mapping is thoroughly understood, we here focus on aspects that become relevant in spatially inhomogeneous situations, such as the effect of boundaries, impurities, superlattices and interfaces. We consider parameter regimes that are relevant for traditional applications of these models, such as electrons in cuprates and manganites, and for more recent applications to atoms in optical lattices. The rate of the mapping as a function of the interaction strength is determined from the Bethe-Ansatz for infinite systems and from numerical diagonalization for finite systems. We show analytically that if translational symmetry is broken through the presence of impurities, the mapping persists and is, in a certain sense, as local as possible, provided the spin-spin interaction between two sites of the Heisenberg model is calculated from the harmonic mean of the onsite Coulomb interaction on adjacent sites of the Hubbard model. Numerical calculations corroborate these findings also in interfaces and superlattices, where analytical calculations are more complicated.Comment: 7 pages, 6 figure

First Report On Dung Beetles In Intra-amazonian Savannahs In Roraima, Brazil

This is the first study to address the dung beetle (Coleoptera: Scarabaeidae: Scarabaeinae) diversity in intra-Amazonian savannahs in the state of Roraima, Brazil. Our aim was to survey the dung beetle fauna associated with these savannahs (regionally called ‘lavrado’), since little is known about the dung beetles from this environment. We conducted three field samples using pitfall traps baited with human dung in savannah areas near the city of Boa Vista during the rainy seasons of 1996, 1997, and 2008. We collected 383 individuals from ten species, wherein six have no previous record in intra-Amazonian savannahs. The most abundant species were Ontherus appendiculatus (Mannerheim, 1829), Canthidium aff. humerale (Germar, 1813), Dichotomius nisus (Olivier, 1789), and Pseudocanthon aff. xanthurus (Blanchard, 1846). We believe that knowing the dung beetles diversity associated with the intra-Amazonian savannahs is ideal for understanding the occurrence and distribution of these organisms in a highly threatened environment, it thus being the first step towards conservation strategy development. © 2016, Universidade Estadual de Campinas UNICAMP. All rights reserved.16

The role of exon shuffling in shaping protein-protein interaction networks

<p>Abstract</p> <p>Background</p> <p>Physical protein-protein interaction (PPI) is a critical phenomenon for the function of most proteins in living organisms and a significant fraction of PPIs are the result of domain-domain interactions. Exon shuffling, intron-mediated recombination of exons from existing genes, is known to have been a major mechanism of domain shuffling in metazoans. Thus, we hypothesized that exon shuffling could have a significant influence in shaping the topology of PPI networks.</p> <p>Results</p> <p>We tested our hypothesis by compiling exon shuffling and PPI data from six eukaryotic species: <it>Homo sapiens</it>, <it>Mus musculus</it>, <it>Drosophila melanogaster</it>, <it>Caenorhabditis elegans</it>, <it>Cryptococcus neoformans</it> and <it>Arabidopsis thaliana</it>. For all four metazoan species, genes enriched in exon shuffling events presented on average higher vertex degree (number of interacting partners) in PPI networks. Furthermore, we verified that a set of protein domains that are simultaneously promiscuous (known to interact to multiple types of other domains), self-interacting (able to interact with another copy of themselves) and abundant in the genomes presents a stronger signal for exon shuffling.</p> <p>Conclusions</p> <p>Exon shuffling appears to have been a recurrent mechanism for the emergence of new PPIs along metazoan evolution. In metazoan genomes, exon shuffling also promoted the expansion of some protein domains. We speculate that their promiscuous and self-interacting properties may have been decisive for that expansion.</p

Quantum mechanics in metric space: wave functions and their densities

Hilbert space combines the properties of two fundamentally different types of mathematical spaces: vector space and metric space. While the vector-space aspects of Hilbert space, such as formation of linear combinations of state vectors, are routinely used in quantum mechanics, the metric-space aspects of Hilbert space are much less exploited. Here we show that a suitable metric stratifies Fock space into concentric spheres. Maximum and minimum distances between wave functions are derived and geometrically interpreted in terms of this metric. Unlike the usual Hilbert-space analysis, our results apply also to the reduced space of only ground-state wave functions and to that of particle densities, each of which forms a metric space but not a Hilbert space. The Hohenberg-Kohn mapping between densities and ground-state wave functions, which is highly complex and nonlocal in coordinate description, is found, for three different model systems, to be very simple in metric space, where it is represented by a monotonic mapping of vicinities onto vicinities. Surprisingly, it is also found to be nearly linear over a wide range of parameters

Dressing approach to the nonvanishing boundary value problem for the AKNS hierarchy

We propose an approach to the nonvanishing boundary value problem for integrable hierarchies based on the dressing method. Then we apply the method to the AKNS hierarchy. The solutions are found by introducing appropriate vertex operators that takes into account the boundary conditions.Comment: Published version Proc. Quantum Theory and Symmetries 7 (QTS7)(Prague, Czech Republic, 2011

Sistema de Controle da Pesca de Mato Grosso do Sul SCPESCA/MS 7 - 2000.

Neste estudo encontram-se as informações sobre a pesca profissional e esportiva coletadas e analisadas pelo SISTEMA DE CONTROLE DA PESCA DE MATO GROSSO DO SUL - SCPESCA/MS em 2000, obtidas para todo o pescado capturado na Bacia do Alto Paraguai - BAP, oficialmente vistoriado pela Polícia Militar Ambiental/MS e desembarcado no Estado. Foi registrado um total de 934t de pescado, onde 33% (306 t) correspondem à pesca profissional e 67% (628 t) à esportiva. As espécies mais capturadas foram: pintado Pseudoplatystoma corruscans (178t; 22,3%), pacu Piaractus mesopotamicus (158 t; 19,8%) e cachara Pseudoplatystoma fasciatum (140 t; 17,6%). Os rios que mais contribuíram foram Paraguai (380 t; 47,6%) e Miranda (179 t; 22,5%). Um total de 42.847 pescadores esportivos visitou o estado de Mato Grosso do Sul, concentrado sobretudo em setembro e outubro, provenientes principalmente de São Paulo (63%). Mensalmente, em mediana, os pescadores profissionais capturaram entre 59,6 e 82,5 kg/pescador.viagem e entre 7,0 e 12,0 kg/pescador.dia, pescado durante 6 a 11 dias/pescaria; os pescadores esportivos capturaram entre 13,5 e 16,0 kg/pescador.viagem e entre 2,8 e 3,8 kg/pescador.dia, pescando durante 4 a 5 dias/pescaria. Comparando-se os dados dos anos de 1994 a 2000, obteve-se um perfil da pesca, identificando-se suas principais tendências.bitstream/item/37414/1/BP38.pd