Positivity, entanglement entropy, and minimal surfaces

The path integral representation for the Renyi entanglement entropies of integer index n implies these information measures define operator correlation functions in QFT. We analyze whether the limit $n\rightarrow 1$, corresponding to the entanglement entropy, can also be represented in terms of a path integral with insertions on the region's boundary, at first order in $n-1$. This conjecture has been used in the literature in several occasions, and specially in an attempt to prove the Ryu-Takayanagi holographic entanglement entropy formula. We show it leads to conditional positivity of the entropy correlation matrices, which is equivalent to an infinite series of polynomial inequalities for the entropies in QFT or the areas of minimal surfaces representing the entanglement entropy in the AdS-CFT context. We check these inequalities in several examples. No counterexample is found in the few known exact results for the entanglement entropy in QFT. The inequalities are also remarkable satisfied for several classes of minimal surfaces but we find counterexamples corresponding to more complicated geometries. We develop some analytic tools to test the inequalities, and as a byproduct, we show that positivity for the correlation functions is a local property when supplemented with analyticity. We also review general aspects of positivity for large N theories and Wilson loops in AdS-CFT.Comment: 36 pages, 10 figures. Changes in presentation and discussion of Wilson loops. Conclusions regarding entanglement entropy unchange

Analytic results on the geometric entropy for free fields

The trace of integer powers of the local density matrix corresponding to the vacuum state reduced to a region V can be formally expressed in terms of a functional integral on a manifold with conical singularities. Recently, some progress has been made in explicitly evaluating this type of integrals for free fields. However, finding the associated geometric entropy remained in general a difficult task involving an analytic continuation in the conical angle. In this paper, we obtain this analytic continuation explicitly exploiting a relation between the functional integral formulas and the Chung-Peschel expressions for the density matrix in terms of correlators. The result is that the entropy is given in terms of a functional integral in flat Euclidean space with a cut on V where a specific boundary condition is imposed. As an example we get the exact entanglement entropies for massive scalar and Dirac free fields in 1+1 dimensions in terms of the solutions of a non linear differential equation of the Painleve V type.Comment: 7 pages, minor change

Area laws in quantum systems: mutual information and correlations

The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. This counterintuitive idea which has its roots in the nonextensive nature of black-hole entropy serves as a guiding principle in the search for the fundamental laws of Planck-scale physics. In this paper we show that a similar phenomenon emerges from the established laws of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law. While the maximal information per unit area depends classically only on the number of microscopic degrees of freedom, it may diverge as the inverse temperature in quantum systems. A rigorous relation between area laws and correlations is established and their explicit behavior is revealed for a large class of quantum many-body states beyond equilibrium systems.Comment: 5 pages, 2 figures, published version with appendi

Operating System Noise in the Linux Kernel

As modern network infrastructure moves from hardware-based to software-based using Network Function Virtualization, a new set of requirements is raised for operating system developers. By using the real-time kernel options and advanced CPU isolation features common to the HPC use-cases, Linux is becoming a central building block for this new architecture that aims to enable a new set of low latency networked services. Tuning Linux for these applications is not an easy task, as it requires a deep understanding of the Linux execution model and the mix of user-space tooling and tracing features. This paper discusses the internal aspects of Linux that influence the Operating System Noise from a timing perspective. It also presents Linux’s osnoise tracer, an in-kernel tracer that enables the measurement of the Operating System Noise as observed by a workload, and the tracing of the sources of the noise, in an integrated manner, facilitating the analysis and debugging of the system. Finally, this paper presents a series of experiments demonstrating both Linux’s ability to deliver low OS noise (in the single-digit μs order), and the ability of the proposed tool to provide precise information about root-cause of timing-related OS noise problems

Hyperspherical entanglement entropy

The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat space-time is shown to equal the conformal anomaly by conformally transforming Euclideanised space--time to a sphere and using already existing formulae for the relevant heat--kernel coefficients after cyclic factoring. The analytical reason for the result is that the conformal anomaly on the lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.Comment: 7 pages. Final revision. Historical comments amended. Minor remarks adde

Bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories

This paper is a review of the main results obtained in a series of papers involving the present authors and their collaborator J L Cardy over the last 2 years. In our work, we have developed and applied a new approach for the computation of the bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories. In most of our work we have also considered these theories to be integrable. Our approach combines two main ingredients: the 'replica trick' and form factors for integrable models and more generally for massive quantum field theory. Our basic idea for combining fruitfully these two ingredients is that of the branch-point twist field. By the replica trick, we obtained an alternative way of expressing the entanglement entropy as a function of the correlation functions of branch-point twist fields. On the other hand, a generalization of the form factor program has allowed us to study, and in integrable cases to obtain exact expressions for, form factors of such twist fields. By the usual decomposition of correlation functions in an infinite series involving form factors, we obtained exact results for the infrared behaviours of the bi-partite entanglement entropy, and studied both its infrared and ultraviolet behaviours for different kinds of models: with and without boundaries and backscattering, at and out of integrability

Apparent digestibility of three diets in the Amiata breed donkey during lactation

The aim of the trial was to evaluate the apparent digestibility of three isonitrogenous and isocaloric diets for lactating donkeys: a diet with 8 kg of hay and 1.5 kg of commercial flaked mixed feed (CM) (Diet 1); a diet with 7 kg of hay and a 2.2 kg of CM (Diet 2) and a diet with 7 kg of hay, 1.5 kg of CM, 200 ml of corn oil and 0.2 kg of soybean meal (Diet 3). Four pluriparous donkeys (309±12 kg BW) at approximately 2-4 months of lactation were used. The trial was conducted according to a 3x3 Latin Square design with 1 or 2 subject per each cell. Feed and faeces samples were analysed for DM, OM, CP, EE, CF, NDF, ADF and gross energy. Acid insoluble ash was used as marker to calculate the apparent digestibility. The apparent digestibility of the main dietary components showed not significant differences among the three diets but generally they were lower in Diet 3. DM intakes of every diet exceeded the esti- mated energy requirement, whereas protein requirements were not significantly satisfied by Diet 1

Faba bean (Vicia faba minor) and pea seeds (Pisum sativum) as protein sources in lactating ewes' diets.

18 Massese lactating ewes, divided into 3 homogeneous groups for parity and milk yield, were used to evaluate the replacement effects of soybean meal by Faba bean (Vicia faba minor) and Pea (Pisum sativum) seeds. During a 70 days trial (beginning after weaning: 30±1.5 days after lambing) animals were fed three isonitrogenous and isocaloric diets. Each diet was characterised by the presence of only one protein feed. The diets consisted of alfalfa hay (1.1 kg/head/d) and a decreasing amount of mixed feed (from 1.1 to 0.7 kg/head/d) to fit animals' requirements. Milk yield, milk chemical composition, animals live weight and BCS, health state and hematochemical parameters were regularly monitored. No diets palatability problems were detected. No significant differences resulted for live weight, BCS, milk yield and milk chemical composition, except for milk protein: higher for faba bean (6.54%) and soybean (6.39%) respect pea (5.66%) diets, P<0.05. No differences resulted for blood parameters too and no clinical signs of illness were observed. Therefore faba bean and pea seeds seem to be able to replace the soybean well