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The tunability of the optical properties of lead halide perovskite nanocrystals makes them highly appealing for applications. Both, halide anion exchange and quantum confinement pave the way for tailoring their band gap energy. For spintronics applications, the Land\'e g-factors of electrons and hole are of great importance. By means of the empirical tight-binding and $\textbf{k}\cdot\textbf{p}$ methods, we calculate them for nanocrystals of the class of all-inorganic lead halide perovskites CsPb$X_3$ ($X = \text{I},\,\text{Br},\,\text{Cl}$). The hole g-factor as function of the band gap follows the universal dependence found for bulk perovskites, while for the electrons a considerable modification is predicted. Based on the $\textbf{k}\cdot\textbf{p}$ analysis we conclude that this difference arises from the interaction of the bottom conduction band with the spin-orbit split electron states. The model predictions are confirmed by experimental data for the electron and hole g-factors in CsPbI3 nanocrystals placed in a glass matrix, measured by time-resolved Faraday ellipticity in a magnetic field at cryogenic temperatures.

The spin physics of perovskite nanocrystals with confined electrons or holes is attracting increasing attention, both for fundamental studies and spintronic applications. Here, stable CsPb(Cl$_{0.5}$Br$_{0.5}$)$_3$ lead halide perovskite nanocrystals embedded in a fluorophosphate glass matrix are studied by time-resolved optical spectroscopy to unravel the coherent spin dynamics of holes and their interaction with nuclear spins of the $^{207}$Pb isotope. We demonstrate the spin mode locking effect provided by the synchronization of the Larmor precession of single hole spins in each nanocrystal in the ensemble that are excited periodically by a laser in an external magnetic field. The mode locking is enhanced by nuclei-induced frequency focusing. An ensemble spin dephasing time $T_2^*$ of a nanosecond and a single hole spin coherence time of $T_2=13\,$ns are measured. The developed theoretical model accounting for the mode locking and nuclear focusing for randomly oriented nanocrystals with perovskite band structure describes the experimental data very well., Comment: Main paper of 9 pages and 3 figures. Supplementary material of 16 pages and 12 figures

The article investigates systems of differential-difference equations of hyperbolic type, integrable in sense of Darboux. The concept of a complete set of independent characteristic integrals underlying Darboux integrability is discussed. A close connection is found between integrals and characteristic Lie-Rinehart algebras of the system. It is proved that a system of equations is Darboux integrable if and only if its characteristic algebras in both directions are finite-dimensional., Comment: 21 pages

ART-XC (Astronomical Roentgen Telescope - X-ray Concentrator) is the hard X-ray instrument with grazing incidence imaging optics on board the Spektr-Roentgen-Gamma (SRG) observatory. The SRG observatory is the flagship astrophysical mission of the Russian Federal Space Program, which was successively launched into orbit around the second Lagrangian point (L2) of the Earth-Sun system with a Proton rocket from the Baikonur cosmodrome on 13 July 2019. The ART-XC telescope will provide the first ever true imaging all-sky survey performed with grazing incidence optics in the 4-30 keV energy band and will obtain the deepest and sharpest map of the sky in the energy range of 4-12 keV. Observations performed during the early calibration and performance verification phase as well as during the on-going all-sky survey that started on 12 Dec. 2019 have demonstrated that the in-flight characteristics of the ART-XC telescope are very close to expectations based on the results of ground calibrations. Upon completion of its 4-year all-sky survey, ART-XC is expected to detect ~5000 sources (~3000 active galactic nuclei, including heavily obscured ones, several hundred clusters of galaxies, ~1000 cataclysmic variables and other Galactic sources), and to provide a high-quality map of the Galactic background emission in the 4-12 keV energy band. ART-XC is also well suited for discovering transient X-ray sources. In this paper, we describe the telescope, results of its ground calibrations, major aspects of the mission, the in-flight performance of ART-XC and first scientific results., Comment: 19 pages, 30 figures, accepted for publication in Astronomy and Astrophysics

Nuclear magnetism in n-doped semiconductors with positive hyperfine constant is revisited. Two kinds of nuclear magnetic ordering can be induced by resident electrons in a deeply cooled nuclear spin system. At positive nuclear spin temperature below a critical value, randomly oriented nuclear spin polarons similar to that predicted by I. Merkulov [I. Merkulov, Physics of the Solid State 40, 930 (1998)] should emerge. These polarons are oriented randomly and within each polaron nuclear and electron spins are aligned antiferromagnetically. At negative nuclear spin temperature below a critical value we predict another type of magnetic ordering - dynamically induced nuclear ferromagnet. This is a long-range ferromagnetically ordered state involving both electrons and nuclei. It can form if electron spin relaxation is dominated by the hyperfine coupling, rather than by the spin-orbit interaction. Application of the theory to the n-doped GaAs suggests that the ferromagnetic order may be reached at experimentally achievable nuclear spin temperature $\Theta_N \approx 0.5$ $\mu$K and lattice temperature $T_L \approx 5$ K., Comment: 12 pages, 6 figures

For the first time the quantum dots CsPbX_3 (X=Cl, Br, I) in the fluorophosphate glasses were prepared. The samples were precipitated by two methods:(i) through self-crystallization during cooling of the glass melt and (ii) heat treatment of the glass. Controlled formation of CsPbX_3 quantum dots was realized by adjustment of cooling rate and heat-treatment conditions. The X-ray diffraction data was confirmed CsPbCl_3(Br_3, I_3) quantum dots formation. It was shown that, CsPbX_3 (X=Cl, I) quantum dots are formed in a cubic modification, while CsPbBr_3 in orthorhombic one. The photoluminescence of quantum dots have high intensity with quantum yield 45-50% and narrow band emission. The combined introduction of two anions (Cl/Br and Br/I) led to the simultaneous formation of two types of quantum dots, and indicates the difficulty of the anion exchange., Comment: 18 pages, 9 figures

We consider the irregular (in the Birkhoff and even the Stone sense) transmission eigenvalue problem of the form $-y''+q(x)y=\rho^2 y,$ $y(0)=y(1)\cos\rho a-y'(1)\rho^{-1}\sin\rho a=0.$ The main focus is on the ''most'' irregular case $a=1,$ which is important for applications. The uniqueness questions of recovering the potential $q(x)$ from transmission eigenvalues were studied comprehensively. Here we investigate the solvability and stability of this inverse problem. For this purpose, we suggest the so-called regularization approach, under which there should first be chosen some regular subclass of eigenvalue problems under consideration, which actually determines the course of the study and even the precise statement of the inverse problem. For definiteness, by assuming $q(x)$ to be a complex-valued function in $W_2^1[0,1]$ possessing the zero mean value and $q(1)\ne0,$ we study properties of transmission eigenvalues and prove local solvability and stability of recovering $q(x)$ from the spectrum along with the value $q(1).$ In Appendices, we provide some illustrative examples of regular and irregular transmission eigenvalue problems, and also obtain necessary and sufficient conditions in terms of the characteristic function for solvability of the inverse problem of recovering an arbitrary real-valued square-integrable potential $q(x)$ from the spectrum, for any fixed $a\in{\mathbb R}.$, Comment: 18 pages

In the article some algebraic properties of nonlinear two-dimensional lattices of the form $u_{n,xy} = f(u_{n+1}, u_n, u_{n-1})$ are studied. The problem of exhaustive description of the integrable cases of this kind lattices remains open. By using the approach, developed and tested in our previous works we adopted the method of characteristic Lie-Rinehart algebras to this case. In the article we derived an effective integrability conditions for the lattice and proved that in the integrable case the function $f(u_{n+1}, u_n, u_{n-1})$ is a quasi-polynomial satisfying the following equation $\frac{\partial^2}{\partial u_{n+1}\partial u_{n-1}}f(u_{n+1}, u_n, u_{n-1})=Ce^{{\alpha}u_n-{\frac{{\alpha}m}{2}}u_{n+1}-{\frac{{\alpha}k}{2}}u_{n-1}},$ where $C$ and $\alpha$ are constant parameters and $k,\,m$ are nonnegative integers.

We develop a new approach to the classification of integrable equations of the form $$ u_{xy}=f(u, u_x, u_y, \triangle_z u \triangle_{\bar z}u, \triangle_{z\bar z}u), $$ where $\triangle_{ z}$ and $\triangle_{\bar z}$ are the forward/backward discrete derivatives. The following 2-step classification procedure is proposed: (1) First we require that the dispersionless limit of the equation is integrable, that is, its characteristic variety defines a conformal structure which is Einstein-Weyl on every solution. (2) Secondly, to the candidate equations selected at the previous step we apply the test of Darboux integrability of reductions obtained by imposing suitable cut-off conditions.

We study Sturm-Liouville operators on closed sets of a special structure, which are sometimes referred as time scales and often appear in modelling various real processes. Depending on the set structure, such operators unify both differential and difference operators. We obtain properties of their spectral characteristics and study inverse problems with respect to them. We prove that the spectral characteristics uniquely determine the operator., Comment: 10 pages

In the article the problem of the integrable classification of nonlinear lattices depending on one discrete and two continuous variables is studied. By integrability we mean the presence of reductions of a chain to a system of hyperbolic equations of arbitrarily high order integrable in the Darboux sense. Darboux integrablity admits a remarkable algebraic interpretation: the Lie-Rinehart algebras related to both characteristic directions corresponding to the reduced system of the hyperbolic equations have to be of finite dimension. A classification algorithm based on the properties of the characteristic algebra is discussed. Some classification results are presented., Comment: IX-th International Conference "SOLITONS, COLLAPSES AND TURBULENCE: Achievements, Developments and Perspectives (SCT-19)'' in honor of Vladimir Zakharov's 80th birthday

We use time-resolved detection of the Hanle effect and polarized photoluminescence with dark intervals to investigate the buildup and decay of the spin polarization of nuclei interacting with donor-bound electrons in $n$-doped GaAs. Strong hyperfine coupling defines the millisecond timescale of the spin dynamics of these nuclei, as distinct from the nuclei far from impurity centers, characterized by a thousand times longer spin-relaxation time. The dynamics of spin polarization and relaxation attributed to the nuclei inside the donor orbit is observed on the time scale from 200 to 425 ms., Comment: 7 pages, 5 figures, minor revision

In the article a classification method for nonlinear integrable equations with three independent variables is discussed based on the notion of the integrable reductions. We call the equation integrable if it admits a large class of reductions being Darboux integrable systems of hyperbolic type equations with two independent variables. The most natural and convenient object to be studied within the frame of this scheme is the class of two dimensional lattices generalizing the well-known Toda lattice. In the present article we deal with the quasilinear lattices of the form $u_{n,xy}=\alpha(u_{n+1} ,u_n,u_{n-1} )u_{n,x}u_{n,y} + \beta(u_{n+1},u_n,u_{n-1})u_{n,x}+\gamma(u_{n+1} ,u_n,u_{n-1} )u_{n,y}+\delta(u_{n+1} ,u_n,u_{n-1})$. We specify the coefficients of the lattice assuming that there exist cutting off conditions which reduce the lattice to a Darboux integrable hyperbolic type system of the arbitrarily high order. Under some extra assumption of nondegeneracy we described the class of the lattices integrable in the sense indicated above. There are new examples in the obtained list of chains., Comment: Submitted to Ufa Mathematical Journal

The spin dynamics of localized donor-bound electrons interacting with the nuclear spin ensemble in $n$-doped GaAs epilayers is studied using nuclear spin polarization by light with modulated circular polarization. We show that the observed build-up of the nuclear spin polarization is a result of competition between nuclear spin cooling and nuclear spin warm-up in the oscillating Knight field. The developed model allows us to explain the dependence of nuclear spin polarization on the modulation frequency and to estimate the equilibration time of the nuclear spin system that appears to be shorter than the transverse relaxation time $T_2$ determined from nuclear magnetic resonance., Comment: Several improvements to v1, 7 pages, 5 figures, corrected list of refs

Photoluminescence polarization is experimentally studied for samples with (In,Ga)As/GaAs selfassembled quantum dots in transverse magnetic field (Hanle effect) under slow modulation of the excitation light polarization from fractions of Hz to tens of kHz. The polarization reflects the evolution of strongly coupled electron-nuclear spin system in the quantum dots. Strong modification of the Hanle curves under variation of the modulation period is attributed to the peculiarities of the spin dynamics of quadrupole nuclei, which states are split due to deformation of the crystal lattice in the quantum dots. Analysis of the Hanle curves is fulfilled in the framework of a phenomenological model considering a separate dynamics of a nuclear field BNd determined by the +/- 12 nuclear spin states and of a nuclear field BNq determined by the split-off states +/- 3/2, +/- 5/2, etc. It is found that the characteristic relaxation time for the nuclear field BNd is of order of 0.5 s, while the relaxation of the field BNq is faster by three orders of magnitude., Comment: 11 pages, 4 figures