Electrical conductivity of hot Abelian plasma with scalar charge carriers

We study the electrical conductivity of hot Abelian plasma containing scalar charge carriers in the leading logarithmic order in coupling constant $\alpha$ using the Boltzmann kinetic equation. The leading contribution to the collision integral is due to the M{\o}ller and Bhabha scattering of scalar particles with a singular cross section in the region of small momentum transfer. Regularizing this singularity by taking into account the hard thermal loop corrections to the propagators of intermediate particles, we derive the second order differential equation which determines the kinetic function. We solve this equation numerically and also use a variational approach in order to find a simple analytical formula for the conductivity. It has the standard parametric dependence on the coupling constant $\sigma\approx 2.38\, T/(\alpha \log\alpha^{-1})$ with the prefactor taking a somewhat lower value compared to the fermionic case. Finally, we consider the general case of hot Abelian plasma with an arbitrary number of scalar and fermionic particle species and derive the simple analytical formula for its conductivity.Comment: 36 pages, 2 figures, 4 table

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

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

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

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

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