The problem of an optimal mapping between Hilbert spaces IN and OUT, based on a series of density matrix mapping measurements ρ^{(l)}→ϱ^{(l)}, l=1⋯M, is formulated as an optimization problem maximizing the total fidelity F=∑_{l=1}^{M}ω^{(l)}F(ϱ^{(l)},∑_{s}B_{s}ρ^{(l)}B_{s}^{†}) subject to probability preservation constraints on Kraus operators B_{s}. For F(ϱ,σ) in the form that total fidelity can be represented as a quadratic form with superoperator F=∑_{s}〈B_{s}|S|B_{s}〉 (either exactly or as an approximation) an iterative algorithm is developed. The work introduces two important generalizations of unitary learning: (1) IN/OUT states are represented as density matrices; (2) the mapping itself is formulated as a mixed unitary quantum channel A^{OUT}=∑_{s}|w_{s}|^{2}U_{s}A^{IN}U_{s}^{†} (no general quantum channel yet). This marks a crucial advancement from the commonly studied unitary mapping of pure states ϕ_{l}=Uψ_{l} to a quantum channel, which allows us to distinguish probabilistic mixture of states and their superposition. An application of the approach is demonstrated on unitary learning of density matrix mapping ϱ^{(l)}=Uρ^{(l)}U^{†}, in this case a quadratic on U fidelity can be constructed by considering sqrt[ρ^{(l)}]→sqrt[ϱ^{(l)}] mapping, and on a quantum channel, where quadratic on B_{s} fidelity is an approximation-a quantum channel is then obtained as a hierarchy of unitary mappings, a mixed unitary channel. The approach can be applied to studying quantum inverse problems, variational quantum algorithms, quantum tomography, and more. A software product implementing the algorithm is available from the authors.

Abstract—Multicomponent polycrystalline TbInxCo2 – x (with х = 0–0.2) solid solutions are prepared for the first time, and their crystal structure and magnetic, magnetocaloric, and magnetostrictive properties are studied. X-ray diffraction patterns taken at room temperature demonstrate mainly the presence of the cubic C15 Laves phase in all samples. As the indium content increases to x = 0.1, the lattice parameter is found to increase; the further increase in the indium content to х = 0.2 leads to a decrease in the lattice parameter. In this case, the Curie temperature TC monotonically increases to 245 K. The isotheral magnetic entropy change ΔSmag is calculated in accordance with magnetic measurements using the thermodynamic Maxwell’s relation. At a magnetic field change from 0 to 1.8 T, the maximum entropy change monotonically decreases and, for composition with x = 0.2, is 1.8 J/(kg К). As the indium content increases to x = 0.05, the volume magnetostriction increases. The further increase in the indium concentration leads to the decrease in the peak values and their shift to high temperatures.

There is no consensus among researchers regarding how phase transitions occur in antiferroelectric (AFE) epitaxial heterostructures, in particular, in heterostructures based on model AFE lead zirconate. The questions about the number of phase transitions in such films and by what mechanism they occur remain controversial. This paper presents a look at the phase transition scenario in two types of epitaxial heterostructures: PbZrO3/Ba[La–Sn]O3/MgO (001) thin films with thicknesses from 25 to 1000 nm and PbZrO3/SrRuO3/SrTiO3 (001) thin film 100 nm thick using the diffuse x-ray scattering in the grazing incidence setup. We register the characteristic butterfly-shaped diffuse scattering (DS) intensity distribution in the HK pseudocubic planes, which corresponds to the anisotropic ferroelectric soft mode. No incommensurate soft mode was observed in the cuts of reciprocal space parallel to the film surface by diffuse scattering. We reproduce the shape of DS distribution at different temperatures by the model based on the dielectric stiffness and the electric polarization correlation tensor in the cubic approximation. Such modeling allows not only to characterize the DS parameters from the challengingly low signal-to-background data set, but also to extract experimentally the sensitivity of the materials with respect to inhomogeneous polarization. While the observed temperature evolution of DS is consistent with the dielectric measurements, the correlation between the DS and the phase transition sequence observed by superstructure reflections is yet to be understood better.

The paper analyzes the structural features of perovskite-like ABO3 type materials responsible for the formation of antiferroelectric phases. For this purpose, the descriptions of some single crystals have been compared using three models: the adapted Slater dipole model (I), the Cowley shell model (II) and the Born - Karman model supplemented with consid- eration of dipole-dipole forces and parameterized basing on ab initio calculations by Ghosez (III). The parameters of model I were found at which qualitative agreement with the data on inelastic X-ray scattering obtained by experiments with lead hafnate was observed. An analysis of all the results led to the conclusion that model I and the Ghosez parameterization confirmed the hypothesis about the key role of the lateral component of the oxygen atoms' polarizability over its axial component for the antiferroelectricity formation. However, model II data did not this.

Aging of the relaxors and PbMg1/3Nb2/3O3in particular was extensively studied in last two decades. Most of the results were related to the low temperature glass-like region. No systematic data around the freezing temperatures were reported. To cover this still missing information we have studied the evolution of the dielectric spectra in the broad frequency region from 10-1 Hz to 106 Hz both below and above the freezing temperatureTf≈240 K. Below freezing temperature the existence of the earlier reported waiting time-frequency scaling at frequencies below ≈50 Hz is confirmed. At higher frequencies this deviation from the scaling is observed that can be tentatively attributed to the complexity of the relaxing entities. AboveTfaging is observed only in the restricted frequency interval below the maximum of the dielectric loss spectrum. The observed effect can be attributed to the hardening and narrowing of the dielectric loss spectra and decreasing of the dielectric strength with time. The explanation is proposed based on the concept of the creation of the degenerate polar nanoregions covering several chemically ordered regions (COR) (multi PNRs-MPNRs). These MPNRs are large compare to the PNRs located at the single CORs and some of them may become frozen resulting in the described spectra changes.

The notion of a near isomorphism is extended from finite-rank torsion-free Abelian groups to some classes of infinite-rank groups. The equivalence of different formulations of this notion for a certain class of countable-rank groups is proved.

The use of mathematical modelling at the early stages of product design makes it possible to substantiate fundamental technical solutions, taking into account all possible (large number) requirements for the product by consumers and operation. At this (early) stage, it is important to use well-tested and convenient tools for designers to create virtual stands and digital twins (DC), confirming compliance, as well as forming the structure of systems and products as a whole. The article discusses a comprehensive methodology for the process of constructing a numerical model of a locomotive for analysing dynamics under various operating conditions. It is based on the top-level structural model (LBM), which is presented in the form of a block diagram and is used at all stages of product design. The required detailing of such a model depends on the actual tasks. The detailed models of the systems that have been developed within the framework of the work are presented.

Maria A. Kniazeva,1, ∗ Alexander E. Ganzha,1 Irena Jankowska-Sumara,2 Marek Pasciak,3 Andrzej Majchrowski,4 Alexey V. Filimonov,5, 1 Andrey I. Rudskoy,1 Krystian Roleder,6 and Roman G. Burkovsky1, † Peter the Great Saint-Petersubrg Polytechnic University, 29 Politekhnicheskaya, 195251, St.-Petersburg, Russia Institute of Physics, Pedagogical University of Cracow, Podchorazych 2, 30-084 Krakow, Poland Institute of Physics, The Academy of Sciences of the Czech Republic, Prague, Czech Republic Institute of Applied Physics, Military University of Technology, ul. Gen. W. Urbanowicza 2, 00-908 Warszawa, Poland Alferov University, 8-3-A Khlopina, 194021, St.-Petersburg, Russia Institute of Physics, University of Silesia, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland

In this work, the structure of the chaotic potential in heterocontacts of III-nitrides, caused by the electrostatic field of charged dislocations, is studied. Taking into account the spatial dispersion of the dielectric response of a two-dimensional electron gas, the amplitude and scale of the chaotic potential in the contact plane are determined. The dependence of the parameters of the chaotic potential on the surface states density and the concentration of dislocations is shown.

The multicomponent Sm 0.2 (Tb,Y) 0.8 Fe 2 system was obtained by the arc melting method, in which atoms with a high magnetic moment of terbium are replaced by yttrium atoms that do not carry a noticeable magnetic moment. In this system, varying not only the composition, but also external factors (temperature, magnetic field, etc.), it is possible to influence competing exchange interactions and observe a number of unique phenomena, such as, for example, the phenomenon of magnetic compensation. Using the method of high-temperature and low-temperature X-ray diffraction, the phase composition and atomic-crystalline structure of the Sm 0.2 (Tb 1-x Y x ) 0.8 Fe 2 alloys (x = 0, 0.2, 0.4, 0.6, 0.8, 1) were studied. The temperature dependences of the unit cell parameters were obtained in a wide temperature range from 80 to 700 K. Thermal expansion was investigated by strain-gauge method. The temperatures of magnetostructural phase transitions are determined, and a magnetic phase diagram is constructed.

In the recent years, a number of pseudo-binary RT2 Laves phases with morphotropic phase transitions, i.e., systems of compounds having a morphotropic phase boundary in the phase diagram, have attracted special attention in the process of searching for compounds with high or, on the contrary, almost zero magnetostriction values. In this work, we study the magnetic and magnetostrictive properties of multicomponent systems based on compounds Tb0.2Dy0.8 – xGdxCo2 and Tb0.2Dy0.8 – xGdxCo1.9Al0.1, in which a morphotropic phase transition is observed when dysprosium is replaced by gadolinium. A relationship between the temperature behavior, the sign and magnitude of magnetostrictive deformations, and the type of cubic lattice distortion of the studied Laves phases is revealed. In the region of magnetic phase transitions, the magnetocaloric effect is investigated.

We investigate the impact of different numbers of positive and negative examples on machine learning for sapphire crystals defects prediction. We obtain the models of crystal growth parameters influence on the sapphire crystal growth. For example, these models allow predicting the defects that occur due to local overcooling of crucible walls in the thermal node leading to the accelerated crystal growth. We also develop the prediction models for obtained crystal weight, blocks, cracks, bubbles formation, and total defect characteristics. The models were trained on all data sets and later tested for generalization on testing sets, which did not overlap the training set. During training and testing, we find the recall, precision of prediction and analyze the correlation among the features. The results have shown that the precision of neural network method for predicting defects formed by local overcooling of the crucible reached 0.94.

This research summarizes the analytical and experimental results of heat-transfer processes influence on defects formation during sapphire crystal growth by horizontal directed crystallization method (HDC). The shape of solid-melt interface significantly influences the process of sapphire crystals growth by this method. We receive the Stefan problem solution for sapphire crystals growth. It allows investigating the crystal growth process and the related factors (thermal stresses on different stages of growth process), their influence on defects formation. We investigate the main reasons for the formation of defective structures of the solid phase of sapphire crystals and the influence of thermal unit construction, the crystal geometry on the quality of the resulting sapphire crystal. We study the structure formation process, impurity distribution, and the nature of the defects in the crystal during it growth.

Оver recent years in the process of searching for compounds with high or almost zero magnetostriction values, a number of pseudo-binary Laves RT2 phases with morphotropic phase transitions are attracted particular attention. That is, systems of compounds with a morphotropic phase boundary in the phase diagram. In this paper, the magnetic and magnetostrictive properties of multicomponent systems of compounds Tb0.2Dy0.8-хGdxCo2 and Tb0.2Dy0.8-хGdxCo1.9Al0.1 in which a morphotropic phase transition is observed when replacing dysprosium with gadolinium have been studied. A relationship between the temperature behavior, the sign and magnitude of magnetostrictive deformations, and the type of distortion of the cubic lattice of the studied Laves phases is revealed. In the region of magnetic phase transitions, the magnetocaloric effect was investigated.

The influence of partial substitution of Co by Al atoms on the magnetocaloric and magnetostrictive properties of the multicomponent Tb-Dy-Gd-Co compounds with a Laves phase structure was investigated. The samples were obtained by arc melting using of high-purity rare-earth metals. The crystal structure of Tb0.2Dy0.8-xGdxCo2-yAly (x = 0.3, 0.4, and 0.5; y = 0 and 0.1) compounds was monitored by powder X-ray diffraction. The magnetostriction and the magnetocaloric effect in external magnetic field up to 12 and 18kOe, respectively, were studied in wide temperature range. The Curie temperature of Al-content compounds increases by an average of 20K, while the magnitudes of the magnetocaloric effect and the magnetostriction slightly decrease. (C) 2017 Elsevier B.V. All rights reserved.

Detailed study of the X-ray diffuse scattering in the paraelectric phase of the PbZr0.985Ti0.015O3 was carried out. We concentrated on the analysis of the scattering peculiarities in the vicinities of M- and R- points of the Brillouin zone. We have observed a critical increase of the diffuse scattering at the position Q approximate to (0.47+h 0.53+k l) slightly aside of M point on cooling to the intermediate phase. We attribute observed critical scattering to a mixed mode containing both oxygen octahedral tilts and antiparallel cationic displacements. Tentative conclusion is made describing earlier reported complicated set of the satellite peaks around M-point as the result of the soft-mode driven incommensurate phase transition.

This article describes a method of manufacturing a deep relief structure of variable depth, based on the chemical etching of glass modified by femtosecond laser radiation. An effective model of deep relief structure of variable depth, suitable for use in optical filters, is proposed.

In this paper, natural heterogeneities of the potential on the degenerated semiconductor surface are discussed as well as the barrier height fluctuations in metal-semiconductor contacts. In the case of electroactive dopant linear screening, characteristic values of chaotic potential amplitudes have been defined. The dependence is shown of these heterogeneities on semiconductor electrophysical parameters.

This paper presents the results of X-ray diffraction studies on a single crystal of lead zirconate titanate PbZr0.993Ti0.007O3 in the region of existence of an intermediate ferroelectric phase. In addition to the known superstructure reflections of the M type qM = $$\left\{ {\frac{1}{2},\frac{1}{2},0} \right\}$$ and the first-order satellite reflections qM + {δ, δ, δ}, unknown second-order satellites have been observed near qM and near the Bragg reflections. Structural model of regular system of antiphase domains is used for diffraction calculation. The model is shown to describe the first- and second-orders satellite reflections in the vicinity of qM, but it cannot explain the appearance of satellites around the main Bragg peaks. A possible origin of the system of the superstructures observed in the intermediate phase is discussed.

In this work, we study photo-induced current transfer through nanocomposite structures consisting of the TiO2 coating activated with plasmonic gold nanoparticles on top of pillar-like structured SiO2. It is shown that the photo-response of the nanocomposite can be adjusted via tuning of the heterostructure topology. Processes at the interface between silicon and noble metal nanoparticle play an important role in charge carrier photo-generation. The high photo-activity in visible part of spectrum has been found in the composite, containing pillar-like silicon dioxide nanostructures [1]. The electron transport via the SiO2 layer from the potential well at the TiO2-SiO2 interface to the n-Si conduction band was explained by electron tunneling mechanism. We present the empirical qualitative model which explains experimental results and helps to separate the contributions of different transport mechanisms.