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

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)

Wettability Of Two-Dimensional Mos2 Layer By Liquid Tin

No-wetting behaviour has been observed for Sn/2D-MoS2/Si100 couple during wetting experiments under conditions used in this study. Nevertheless, the degradation of MoS2 due to its interaction with molten Sn drop took place as evidenced by local EDS analysis and Raman spectroscopy. These findings should be taken into consideration in the design of innovative composite materials and new concept electronic devices using 2D-MoS2 types of materials for liquid-assisted processes

9 ×\times 4 = 6 ×\times 6: Understanding the quantum solution to the Euler's problem of 36 officers

The famous combinatorial problem of Euler concerns an arrangement of $36$ officers from six different regiments in a $6 \times 6$ square array. Each regiment consists of six officers each belonging to one of six ranks. The problem, originating from Saint Petersburg, requires that each row and each column of the array contains only one officer of a given rank and given regiment. Euler observed that such a configuration does not exist. In recent work, we constructed a solution to a quantum version of this problem assuming that the officers correspond to quantum states and can be entangled. In this paper, we explain the solution which is based on a partition of 36 officers into nine groups, each with four elements. The corresponding quantum states are locally equivalent to maximally entangled two-qubit states, hence each officer is entangled with at most three out of his $35$ colleagues. The entire quantum combinatorial design involves $9$ Bell bases in nine complementary $4$-dimensional subspaces.Comment: 26 page

Wettability of the System of Cast Iron and Magnesia Ceramics with Graphite

In this paper examinations of high-temperature wetting tests of 3 systems of liquid alloy – cast iron in contact with ceramic materials: magnesia ceramics in combination with natural graphite were presented. After wettability testing, the microscopic observations of the morphology of the sample surface and the cross-section microstructure with the chemical composition in micro-areas were examined. One of the objective of this work was also to verify whether the graphite content would affect the wettability of the magnesia ceramics. The study of high-temperature wetting kinetics of the liquid alloy in contact with the ceramic material, by the "sessile drop" method with capillary purification (CP) procedure was conducted. Under the test conditions, at a temperature of 1450°C and time 15 minutes, all 3 experimental systems showed a non-wetting behaviour. The average contact angle for the system with cast iron drop on magnesia ceramics was 140°, on magnesia ceramics with 10 parts per weight of graphite was 137° and on magnesia ceramics with 30 parts per weight of graphite - 139°. Microscopic observations revealed that in the case of the sample consisting of the cast iron drop on the substrate with magnesia ceramics, the formation of fine separations was not observed, unlike the systems with the substrate with magnesia ceramics and the addition of natural graphite. Numerous, fine droplets accumulate on the graphite flakes and consist mainly of Si as well as Fe and O. On the other hand, the rough MgO grains have a gray, matt surface, without fine separations. The conducted observations indicate the mechanical nature of the bonding - liquid metal penetrates into the pores of the rough ceramics of the substrate. However, in the case of systems of cast iron drop with magnesia ceramics and addition of graphite, probably the adhesive connection and the physical attraction of elements derived from cast iron drop with the flake graphite appeared as well

9 × 4 = 6 × 6: Understanding the quantum solution to Euler's problem of 36 officers

The famous combinatorial problem of Euler concerns an arrangement of 36 officers from six different regiments in a 6×6 square array. Each regiment consists of six officers each belonging to one of six ranks. The problem, originating from Saint Petersburg, requires that each row and each column of the array contains only one officer of a given rank and given regiment. Euler observed that such a configuration does not exist. In recent work, we constructed a solution to a quantum version of this problem assuming that the officers correspond to superpositions of quantum states. In this paper, we explain the solution which is based on a partition of 36 officers into nine groups, each with four elements. The corresponding quantum states are locally equivalent to maximally entangled two-qubit states, hence each quantum officer is represented by a superposition of at most 4 classical states. The entire quantum combinatorial design involves 9 Bell bases in nine complementary 4-dimensional subspaces

Thirty-six entangled officers of Euler : quantum solution to a classically impossible problem

The negative solution to the famous problem of $36$ officers of Euler implies that there are no two orthogonal Latin squares of order six. We show that the problem has a solution, provided the officers are entangled, and construct orthogonal quantum Latin squares of this size. As a consequence, we find an example of the long-elusive Absolutely Maximally Entangled state AME$(4,6)$ of four subsystems with six levels each, equivalently a $2$-unitary matrix of size $36$, which maximizes the entangling power among all bipartite unitary gates of this dimension, or a perfect tensor with four indices, each running from one to six. This special state deserves the appellation golden AME state as the golden ratio appears prominently in its elements. This result allows us to construct a pure nonadditive quhex quantum error detection code $(\!(3,6,2)\!)_6$, which saturates the Singleton bound and allows one to encode a $6$-level state into a triplet of such states.Comment: 14 pages, 12 figure

Wetting behavior and reactivity of molten silicon with h-BN substrate at ultrahigh temperatures up to 1750 °C

For a successful implementation of newly proposed silicon-based latent heat thermal energy storage systems, proper ceramic materials that could withstand a contact heating with molten silicon at temperatures much higher than its melting point need to be developed. In this regard, a non-wetting behavior and low reactivity are the main criteria determining the applicability of ceramic as a potential crucible material for long-term ultrahigh temperature contact with molten silicon. In this work, the wetting of hexagonal boron nitride (h-BN) by molten silicon was examined for the first time at temperatures up to 1750 C. For this purpose, the sessile drop technique combined with contact heating procedure under static argon was used. The reactivity in Si/h-BN system under proposed conditions was evaluated by SEM/EDS examinations of the solidified couple. It was demonstrated that increase in temperature improves wetting, and consequently, non-wetting-to-wetting transition takes place at around 1650 C. The contact angle of 90 ± 5 is maintained at temperatures up to 1750 C. The results of structural characterization supported by a thermodynamic modeling indicate that the wetting behavior of the Si/h-BN couple during heating to and cooling from ultrahigh temperature of 1750 C is mainly controlled by the substrate dissolution/reprecipitation mechanism