Induced Ginibre ensemble of random matrices and quantum operations

A generalisation of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the ensemble of rectangular Gaussian matrices via a quadratisation procedure. We derive the joint probability density of eigenvalues for such induced Ginibre ensemble and study various spectral correlation functions for complex and real matrices, and analyse universal behaviour in the limit of large dimensions. In this limit the eigenvalues of the induced Ginibre ensemble cover uniformly a ring in the complex plane. The real induced Ginibre ensemble is shown to be useful to describe statistical properties of evolution operators associated with random quantum operations, for which the dimensions of the input state and the output state do differ.Comment: 2nd version, 34 pages, 5 figure

Random Bistochastic Matrices

Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the probability measure induced into the Birkhoff polytope of bistochastic matrices by applying the Sinkhorn algorithm to a given ensemble of random stochastic matrices. For matrices of order N=2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the Dirichlet distribution. For arbitrary $N$ we construct an initial ensemble of stochastic matrices which allows one to generate random bistochastic matrices according to a distribution locally flat at the center of the Birkhoff polytope. The value of the probability density at this point enables us to obtain an estimation of the volume of the Birkhoff polytope, consistent with recent asymptotic results.Comment: 22 pages, 4 figure

Wetting behaviour and reactivity between liquid Gd and ZrO2 substrate

The wetting behavior and reactivity between molten pure Gd and polycrystalline 3YSZ substrate (ZrO2 stabilized with 3 wt% of Y2O3)were experimentally determined by a sessile drop method using a classical contact heating coupled with drop pushing procedure. The test was performed under an inert flowing gas atmosphere (Ar) at two temperatures of 1362°C and 1412°C. Immediately after melting (Tm=1341°C), liquid Gd did not wet the substrate forming a contact angle of θ=141°. The non-wetting to wetting transition (θ < 90°) took place after about 110 seconds of interaction and was accompanied by a sudden decrease in the contact angle value to 67°. Further heating of the couple to 1412 °C did not affect wetting (θ=67°±1°). The solidified Gd/3YSZ couple was studied by means of optical microscopy and scanning electron microscopy coupled with X-ray energy dispersive spectroscopy. Structural investigations revealed that the wettability in the Gd/3YSZ system is of a reactive nature associated with the formation of a continuous layer of a wettable reaction product Gd2Zr2O7

Wettability and reactivity of ZrB2 substrates with liquid Al

Wetting characteristics of the Al/ZrB2 system were experimentally determined by the sessile drop method with application of separate heating of the ZrB2 and Al samples and combined with in situ cleaning of Al drop from native oxide film directly in vacuum chamber. The tests were performed in ultrahigh vacuum of 10−6 mbar at temperatures 710, 800, and 900 °C as well as in flowing inert gas (Ar) atmosphere at 1400 °C. The results evidenced that liquid Al does not wet ZrB2 substrate at 710 and 800 °C, forming high contact angles (θ) of 128° and 120°, respectively. At 900 °C, wetting phenomenon (θ < 90°) occurs in 29th minute and the contact angle decreases monotonically to the final value of 80°. At 1400 °C, wetting takes place immediately after drop deposition with a fast decrease in the contact angle to 76°. The solidified Al/ZrB2 couples were studied by scanning and transmission electron microscopy coupled with x-ray energy diffraction spectroscopy. Structural characterization revealed that only in the Al/ZrB2 couple produced at the highest temperature of 1400 °C new phases (Al3Zr, AlB2 and α-Al2O3) were formed

Experimentally feasible measures of distance between quantum operations

We present two measures of distance between quantum processes based on the superfidelity, introduced recently to provide an upper bound for quantum fidelity. We show that the introduced measures partially fulfill the requirements for distance measure between quantum processes. We also argue that they can be especially useful as diagnostic measures to get preliminary knowledge about imperfections in an experimental setup. In particular we provide quantum circuit which can be used to measure the superfidelity between quantum processes. As the behavior of the superfidelity between quantum processes is crucial for the properties of the introduced measures, we study its behavior for several families of quantum channels. We calculate superfidelity between arbitrary one-qubit channels using affine parametrization and superfidelity between generalized Pauli channels in arbitrary dimensions. Statistical behavior of the proposed quantities for the ensembles of quantum operations in low dimensions indicates that the proposed measures can be indeed used to distinguish quantum processes.Comment: 9 pages, 4 figure

A Comparison of Machine Learning and Classical Demand Forecasting Methods: A Case Study of Ecuadorian Textile Industry

[EN] This document presents a comparison of demand forecasting methods, with the aim of improving demand forecasting and with it, the production planning system of Ecuadorian textile industry. These industries present problems in providing a reliable estimate of future demand due to recent changes in the Ecuadorian context. The impact on demand for textile products has been observed in variables such as sales prices and manufacturing costs, manufacturing gross domestic product and the unemployment rate. Being indicators that determine to a great extent, the quality and accuracy of the forecast, generating also, uncertainty scenarios. For this reason, the aim of this work is focused on the demand forecasting for textile products by comparing a set of classic methods such as ARIMA, STL Decomposition, Holt-Winters and machine learning, Artificial Neural Networks, Bayesian Networks, Random Forest, Support Vector Machine, taking into consideration all the above mentioned, as an essential input for the production planning and sales of the textile industries. And as a support, when developing strategies for demand management and medium-term decision making of this sector under study. Finally, the effectiveness of the methods is demonstrated by comparing them with different indicators that evaluate the forecast error, with the Multi-layer Neural Networks having the best results with the least error and the best performance.The authors are greatly grateful by the support given by the SDAS Research Group (https://sdas-group.com/).Lorente-Leyva, LL.; Alemany Díaz, MDM.; Peluffo-Ordóñez, DH.; Herrera-Granda, ID. (2021). 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One-component plasma on a spherical annulus and a random matrix ensemble

The two-dimensional one-component plasma at the special coupling \beta = 2 is known to be exactly solvable, for its free energy and all of its correlations, on a variety of surfaces and with various boundary conditions. Here we study this system confined to a spherical annulus with soft wall boundary conditions, paying special attention to the resulting asymptotic forms from the viewpoint of expected general properties of the two-dimensional plasma. Our study is motivated by the realization of the Boltzmann factor for the plasma system with \beta = 2, after stereographic projection from the sphere to the complex plane, by a certain random matrix ensemble constructed out of complex Gaussian and Haar distributed unitary matrices.Comment: v2, typos and references corrected, 24 pages, 1 figur

Random repeated quantum interactions and random invariant states

We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in detail. One is provided by considering Haar-distributed unitaries to describe each interaction between $\mathcal{H}$ and $\mathcal{K}_n$. The other involves random quantum states describing each copy $\mathcal{K}_n$. In the limit of a large number of interactions, we present convergence results for the asymptotic state of $\mathcal{H}$. This is achieved by studying spectral properties of (random) quantum channels which guarantee the existence of unique invariant states. Finally this allows to introduce a new physically motivated ensemble of random density matrices called the \emph{asymptotic induced ensemble}

The Way to a Man's Heart Is through His Stomach: What about Horses?

International audienceBACKGROUND: How do we bond to one another? While in some species, like humans, physical contact plays a role in the process of attachment, it has been suggested that tactile contact's value may greatly differ according to the species considered. Nevertheless, grooming is often considered as a pleasurable experience for domestic animals, even though scientific data is lacking. On another hand, food seems to be involved in the creation of most relationships in a variety of species. METHODOLOGY/PRINCIPAL FINDINGS: In this study, we used the horse training context to test the effects of food versus grooming during repeated human-horse interactions. The results reveal that food certainly holds a key role in the attachment process, while tactile contact was here clearly insufficient for bonding to occur. CONCLUSION/SIGNIFICANCE: This study raises important questions on the way tactile contact is perceived, and shows that large inter-species differences are to be expected