Universality of spectra for interacting quantum chaotic systems

We analyze a model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements. Under the condition of strong classical chaos and strong decoherence due to large coupling with the measurement device, the spectra of the evolution operator exhibit an universal behavior. A generic spectrum consists of a single eigenvalue equal to unity, which corresponds to the invariant state of the system, while all other eigenvalues are contained in a disk in the complex plane. Its radius depends on the number of the Kraus measurement operators, and determines the speed with which an arbitrary initial state converges to the unique invariant state. These spectral properties are characteristic of an ensemble of random quantum maps, which in turn can be described by an ensemble of real random Ginibre matrices. This will be proven in the limit of large dimension.Comment: 11 pages, 10 figure

Multi-Unitary Complex Hadamard Matrices

We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of $2k$ subsystems with $d$ levels each to the set of complex Hadamard matrices of order $N=d^k$. To this end, we investigate possible subsets of such matrices which are, dual, strongly dual ($H=H^{\rm R}$ or $H=H^{\rm\Gamma}$), two-unitary ($H^R$ and $H^{\Gamma}$ are unitary), or $k$-unitary. Here $X^{\rm R}$ denotes reshuffling of a matrix $X$ describing a bipartite system, and $X^{\rm \Gamma}$ its partial transpose. Such matrices find several applications in quantum many-body theory, tensor networks and classification of multipartite quantum entanglement and imply a broad class of analytically solvable quantum models in $1+1$ dimensions.Comment: 18 pages, no figure

Mubs and Hadamards of Order Six

We report on a search for mutually unbiased bases (MUBs) in 6 dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set of all complex Hadamard matrices of the given order, and we introduce a natural notion of distance between bases in Hilbert space. This allows us to draw a detailed map of where in the landscape the MUB triplets are situated. We use available tools, such as the theory of the discrete Fourier transform, to organise our results. Finally we present some evidence for the conjecture that there exists a four dimensional family of complex Hadamard matrices of order 6. If this conjecture is true the landscape in which one may search for MUBs is much larger than previously thought.Comment: 33 pages, 3 figures. References added in v

Tensor rank and entanglement of pure quantum states

The rank of a tensor is analyzed in context of quantum entanglement. A pure quantum state $\bf v$ of a composite system consisting of $d$ subsystems with $n$ levels each is viewed as a vector in the $d$-fold tensor product of $n$-dimensional Hilbert space and can be dentified with a tensor with $d$ indices, each running from $1$ to $n$. We discuss the notions of the generic rank and the maximal rank of a tensor and review results known for the low dimensions. Another variant of this notion, called the border rank of a tensor, is shown to be relevant for characterization of orbits of quantum states generated by the group of special linear transformations. A quantum state ${\bf v}$ is called {\sl entangled}, if it {\sl cannot} be written in the product form, ${\bf v} \ne {\bf v}_1 \otimes {\bf v}_2 \otimes \cdots \otimes {\bf v}_d$, what implies correlations between physical subsystems. A relation between various ranks and norms of a tensor and the entanglement of the corresponding quantum state is revealed.Comment: 46 page

Interfacial Phenomena between Liquid Si-rich Si-Zr Alloys and Glassy Carbon

To succeed in the design and optimization of liquid-assisted processes such as reactive infiltration for the fabrication of tailored refractory SiC/ZrSi2 composites, the interfacial phenomena that occur when Si-rich Si-Zr alloys are in contact with glassy carbon (GC) were investigated for the first time by the sessile drop method at T = 1450 °C. Specifically, two different Si-rich Si-Zr alloys were selected, and the obtained results in terms of wettability, spreading kinetics, reactivity, and developed interface microstructures were compared with experimental observations that were previously obtained for the liquid Si-rich, Si-Zr, near-eutectic composition (i.e., Si-10 at.%Zr) that was processed under the same operating conditions. The increase of the Si content only weakly affected the overall phenomena that were observed at the interface. From the practical point of view, this means that even Si-Zr alloys with a higher Si content, with respect to the near eutectic alloy, may be potentially used as infiltrant materials.The work performed at CNR-ICMATE was supported by National Science Center of Poland through POLONEZ project number UMO-2016/23/P/ST8/01916. This project is carried out under POLONEZ-3 program which has received funding from European Union’s Horizon 2020 research and innovation program under Marie Skłodowska-Curie grant agreement. No 665778. The work performed by JN was funded by the Spanish “Ministerio de Economía y Competitividad” (Grant MAT2017-86992-R) and action Mobility of Alicante University

Improved methodological concepts for processing liquid Mg at high temperature

Abstract In this paper, new improvements of methodological concepts upon examining wettability of high vapor pressure liquid metal systems (e.g. Mg-based alloys) in contact with refractory materials, are presented and discussed. In this regard, high-temperature experiments on molten magnesium (Mg) in contact with graphite as a refractory substrate, were performed by utilizing a newly developed testing device and by applying a suitable experimental procedure. The wetting experiments were carried out by the sessile drop method and under identical testing conditions (700 °C/10 min under a protective gas atmosphere). Two different procedures were applied: the classical contact heating (CH) or a newly introduced capillary purification (CP) one. The contact angle behaviors observed under the same conditions were strongly influenced by the applied procedure. Specifically, in the case of using the CH procedure, a presence of native surface oxide layer on the metal surface hinders the observations of melting process, making not possible to experimentally determine the wetting kinetics curve θ=f(t). Contrarily, during the wetting test performed on the Mg/graphite couple by applying the CP procedure, the native surface oxide layer was mechanically removed during the squeezing of the molten Mg through the hole of a capillary. Indeed, an oxide-free squeezed Mg-drop with regular and spherical shape was successfully obtained and dispensed on the graphite substrate. Consequently, the reliable contact angle value around θ=150° for the Mg/graphite system, was measured within the wetting test

The Effect of Boron Content on Wetting Kinetics in Si-B Alloy/h-BN System

In this work, the effect of boron content on the high-temperature wetting behavior in the Si-B alloy/h-BN systems was experimentally examined. For this reason, hypoeutectic, eutectic and hypereutectic Si-B alloys (Si-1B, Si-3.2B and Si-5.7B wt.%, respectively) were produced by electric arc melting method and then subjected to sessile drop/contact heating experiments with polycrystalline h-BN substrates, at temperatures up to 1750 °C. Similar to pure Si/h-BN system, wetting kinetics curves calculated on a basis of in situ recorded drop/substrate images point toward non-wetting behavior of all selected Si-B alloy/h-BN couples. The highest contact angle values of ~ 150° were obtained for hypoeutectic and eutectic Si-B alloys in the whole examined temperature range. © 2018, The Author(s)

Random Quantum Operations

We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Phi associated with a given quantum map are investigated and a quantum analogue of the Frobenius-Perron theorem is proved. We derive a general formula for the density of eigenvalues of Phi and show the connection with the Ginibre ensemble of real non-symmetric random matrices. Numerical investigations of the spectral gap imply that a generic state of the system iterated several times by a fixed generic map converges exponentially to an invariant state

Block-Circulant Complex Hadamard Matrices

A new method of obtaining a sequence of isolated complex Hadamard matrices (CHM) for dimensions $N\geqslant 7$, based on block-circulant structures, is presented. We discuss, several analytic examples resulted from a modification of the Sinkhorn algorithm. In particular, we explicitly present new isolated matrices of orders $9$, $10$ and $11$, which elements are not roots of unity, and also several new multiparametric families of order $10$. We note novel connections between certain eight-dimensional matrices and provide new insights towards classification of CHM for $N\geqslant 7$. These contributions can find real applications in Quantum Information Theory and constructions of new families of Mutually Unbiased Bases or Unitary Error Bases.Comment: 21 pages, no figure

Collocations in the language of politics in Germany, Austria and Switzerland

Tematem niniejszej pracy licencjackiej p.t. Kollokationen in der Sprache der Politik in Deutschland, Österreich und der Schweiz jest wskazanie różnic między kolokacjami leksykalnymi w języku politycznym krajów niemieckojęzycznych.Praca jest podzielona na pięć rozdziałów, z których każdy dotyczy innego aspektu różnic pomiędzy wariantami języka niemieckiego, a także teorii kolokacji.Rozdział pierwszy opisuje pluricentryczny charakter języka niemieckiego, jak i terminy związane z pojęciem pluricentryzmu.Rozdział drugi wskazuje główne różnice pomiędzy wariantami języka w Niemczech, Austrii i Szwajcarii. Rozdział podzielony jest na trzy podrozdziały. Każdy z nich opisuje inny wariant języka niemieckiego.Rozdział trzeci skupia się na teorii kolokacji. Podrozdział pierwszy opisuje historię terminu i analizuje badania Waltera Porziga, Johna Ruperta Firtha, Eugenio Coseriu, a także w dziedzinie polskiego językoznawstwa Stanisława Skorupki i Haliny Kurkowskiej. W kolejnych podrozdziałach przedstawiono definicję terminu kolokacja oraz opis struktury kolokacji. Rozdział czwarty zawiera analizę kolokacji leksykalnych z uwzględnieniem różnic wynikających z systemu politycznego w poszczególnych krajach niemieckojęzycznych.. Wnioski, zawarte w rozdziale piątym, eksponują wpływ różnicy systemów politycznych, a także różnic kulturowych i historycznych na sferę językową.The primary purpose of this thesis Kollokationen in der Sprache der Politik in Deutschland, Österreich und der Schweiz is to identify the differences among collocations in standard varieties of German in the language of politics. The graduation thesis is composed of five chapters, each of them dealing with different aspect of three varieties of German in Germany, Austria and Switzerland and the theory of collocations.Chapter 1 describes German as a pluricentric language and shows therms connected to the topic of pluricenticity.Chapter 2 examines the main differences in the varieties of German in Germany, Austria and Switzerland. The chapter is subdivided into three parts. Each of them describes one variety of German.Chapter 3 concentrates on the theory of collocations. Part 1 describes the history of the term and analyses investigations of Walter Porzig, John Rupert Firth, Eugenio Coseriu and some Polish researchers. Part 2 focuses on the definition of the term collocation. The 3rd part describes the structure of collocation whereas part 4 examines the terms base (basis) and collocator (Kollokator).Chapter 4 focuses on the language of politics. Part 1 describes political systems in Germany, Austria and Switzerland. Part 2 shows the linguistic differences among theese countries. The 3rd part gives examles for those differences.Conclusions are drawn in Chapter 5. The main aim of the graduation thesis has been reached. The author proposes that political system, historical and cultural differences and pluricentricity itself as the main reasons for linguistic differences in the language of politics.Das Ziel der Untersuchung ist die Darstellung der Gründe für diese Differenzen. Im Rahmen dieser Arbeit soll beantwortet werden, was die Sprache der Politik in den deutschsprachigen Ländern beeinflusst. Die Arbeit wird in fünf Kapitel aufgeteilt. Am Anfang, im ersten und zweiten Kapitel, wird der plurizentrische Charakter der deutschen Sprache und ihre Vollzentren beschrieben. Im dritten Kapitel wird die Theorie der Kollokationen, die Geschichte und Definition des Begriffs dargestellt. Das vierte Kapitel ist der Analyse der Kollokationen in der Sprache der Politik in Deutschland, Österreich und in der Schweiz gewidmet. Es werden die Teutonismen, Austriazismen und Helvetismen im Bereich der Kollokationen klassifiziert und in Bezug auf das politische Leben in einzelnen deutschsprachigen Ländern analysiert. Anschließend werden die Schlussfolgerungen gezogen, die die Zusammenhänge zwischen der Sprache der Politik und der Realität einzelner Länder hervorheben