Supercritical electric dipole and migration of electron wave function in graphene

We study the Dirac equation for quasiparticles in gapped graphene with two oppositely charged impurities by using the technique of linear combination of atomic orbitals and variational Galerkin--Kantorovich method. We show that for sufficiently large charges of impurities the wave function of the occupied electron bound state of the highest energy changes its localization from the negatively charged impurity to the positively charged one as the distance between the impurities increases. This migration of the electron wave function of supercritical electric dipole is a generalization of the familiar phenomenon of the atomic collapse of single charged impurity to the case where electron-hole pairs are spontaneously created from vacuum in bound states with charge impurities thus partially screening them.Comment: 8 pages, 6 Figures, and video; submitted to Europhysics Letter

Investigation of the influence of technological conditions of microarc oxidation of magnesium alloys on their structural state and mechanical properties

Наведені дослідження структури і властивостей покриттів, отриманих при мікродуговій обробці на магнієвому сплаві. Обробка проводилася при анодно-катодному режимі в лужному електроліті з різними домішками. Показана можливість формування кристалічних оксидних покриттів різного фазового складу (MgO, MgAl₂O₄, Mg₂Sі₄, Mg₃(PO₄)₂) товщиною до 300 мкм, що мають високу адгезію з основою, гарні захисні властивості і високу твердість, яка досягає 6,6 ГПа

Influence of backreaction of electric fields and Schwinger effect on inflationary magnetogenesis

We study the generation of electromagnetic fields during inflation when the conformal invariance of Maxwell's action is broken by the kinetic coupling $f^{2}(\phi)F_{\mu\nu}F^{\mu\nu}$ of the electromagnetic field to the inflaton field $\phi$. We consider the case where the coupling function $f(\phi)$ decreases in time during inflation and, as a result, the electric component of the energy density dominates over the magnetic one. The system of equations which governs the joint evolution of the scale factor, inflaton field, and electric energy density is derived. The backreaction occurs when the electric energy density becomes as large as the product of the slow-roll parameter $\epsilon$ and inflaton energy density, $\rho_{E}\sim \epsilon \rho_{\rm inf}$. It affects the inflaton field evolution and leads to the scale-invariant electric power spectrum and the magnetic one which is blue with the spectral index $n_{B}=2$ for any decreasing coupling function. This gives an upper limit on the present-day value of observed magnetic fields below $10^{-22}\,{\rm G}$. It is worth emphasizing that since the effective electric charge of particles $e_{\rm eff}=e/f$ is suppressed by the coupling function, the Schwinger effect becomes important only at the late stages of inflation when the inflaton field is close to the minimum of its potential. The Schwinger effect abruptly decreases the value of the electric field, helping to finish the inflation stage and enter the stage of preheating. It effectively produces the charged particles, implementing the Schwinger reheating scenario even before the fast oscillations of the inflaton. The numerical analysis is carried out in the Starobinsky model of inflation for the powerlike $f\propto a^{\alpha}$ and Ratra-type $f=\exp(\beta\phi/M_{p})$ coupling functions.Comment: 21 pages, 8 figure

Electron states in the field of charged impurities in two-dimensional Dirac systems

We review the theoretical and experimental results connected with the electron states in two-dimensional Dirac systems paying a special attention to the atomic collapse in graphene. Two-electron bound states of a Coulomb impurity are considered too. A rather subtle role of a magnetic field in the supercritical charge problem in graphene is discussed. The electron states in the field of two equally charged impurities are studied and the conditions for supercritical instability to occur are determined. It is shown that the supercriticality of novel type is realized in gapped graphene with two unlikely charged impurities. For sufficiently large charges of impurities, it is found that the wave function of the occupied electron bound state of the highest energy changes its localization from the negatively charged impurity to the positively charged one as the distance between the impurities increases. The specifics of the atomic collapse in bilayer graphene is considered and it is shown that the atomic collapse in this material is not related to the phenomenon of the fall-to-center.Comment: Review Article, 39 pages, 14 figures. arXiv admin note: text overlap with arXiv:1311.0064, arXiv:1401.5992, arXiv:1611.05221, arXiv:1510.02890, arXiv:1406.5770 by other author

Problem statement of dynamic creep for isotropic and оrthotropic bodies

Mathematical problem statement of dynamic creep for isotropic and orthotropic bodies is presented in the paper. The cyclic creep-damage theory of Breslavsky-Morachkovsky is used. Numerical methods for the solution of such creep problems is considered, where the mixed variational functional and RFM (Rvachov’s Functions method), or finite element method (FEM), are applied. Numerical results of the creep problem analysis for plate with centered hole under tension are given

Influence of the thermal factor on the composition of electron-beam high-entropy ALTiVCrNbMo coatings

This paper reports results of studying the element and phase compositions of electron-beam coatings based on the high-entropy alloy AlTiVCrNbMo, depending on the deposition temperature (in the range of 300...700 °С). The high-entropy alloys were melted in an arc furnace in an atmosphere of high-purity argon. Vacuum condensates of the high-entropy alloy (AlTiVCrNbMo) with a thickness of 3–5 µm were obtained in the vacuum setup UVN-2M-1 at a working vacuum of 5·10-5 mТоrr. The alloy evaporation was performed from the water-cooled ingot mold using an electron-beam gun with a power of 5 kW. Condensation of vapors of all the elements of the alloy was performed onto copper substrates at temperatures of 300, 500, 700 °C. Based on analysis of the element composition of materials of the target made of the high-entropy six-element alloy AlTiVCrNbMo and electron-beam coatings, based on it, we established the critical parameter (specific heat of vaporization of an element) that defined a selective change in the element composition. In accordance with a characteristic change in the composition of coatings of the multi-element high-entropy alloy, 3 groups of elements were distinguished: with a specific heat of evaporation of 280...350 kJ/mol (group 1), 420…460 kJ/mol (group 2), and 590…680 kJ/mol (group 3). It was shown that the formation of a single-phase coating of the high-entropy alloy (based on BCC of the crystalline lattice) occurs at the higher deposition temperature of 500...700 °C when the coating consists of not less than 5 elements. It was established that based on the conditions for an electron-beam process of materials formation, the results obtained can be divided into two types: those determined by the condition of evaporation of the target and those determined by the conditions of coating deposition. The density of flows of elements, evaporated from the target, is determined by their specific heat of evaporation. However, the ratio of atoms in the flow, derived in this way, may not be retained in the formed coating due to the secondary evaporation of elements from the growth surface. The obtained results allow us to substantiate principles for the selection of components for achieving the optimal element and phase compositions of high-entropy alloys.На основі аналізу елементного складу матеріалів мішені з високоентропійного шестиелементного сплаву AlTiVCrNbMo і електронно-променевих покриттів на його основі встановлено критичний параметр (питома теплота випаровування елемента), який визначає селективну зміну елементного складу. Показано, що формування однофазного покриття високоентропійного сплаву відбувається, коли до складу покриття входить не менше 5 елементів. Отримані результати дозволяють обґрунтувати принципи підбору компонент для досягнення оптимальних елементного та фазового складу високоентропійних сплавів

Evolution of the Primordial Axial Charge across Cosmic Times

We investigate collisional decay of the axial charge in an electron-photon plasma at temperatures 10 MeV - 100 GeV. We demonstrate that the decay rate of the axial charge is first order in the fine-structure constant $\Gamma_{\rm flip}\propto \alpha m_{e}^{2}/T$ and thus orders of magnitude greater than the naive estimate which has been in use for decades. This counterintuitive result arises through infrared divergences regularized at high temperature by environmental effects. The decay of axial charge plays an important role in the problems of leptogenesis and cosmic magnetogenesis.Comment: 7 pages, 3 figures + Supplementary Material (3 pages