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Saint Petersburg, Russia

The Herzen State Pedagogical University of Russia is one of the largest universities in Russia. Located in Saint Petersburg, it operates 20 faculties and more than 100 departments. Embroidered in its structure are the Institute of Pre-University Courses, the Institute of Continuous Professional Development, and the Pedagogical Research Center. The university is named after the Russian writer and philosopher Alexander Herzen. Wikipedia.


Vertogradov V.D.,Herzen State Pedagogical University
Gravitation and Cosmology | Year: 2016

The gravitational collapse in generalized Vaidya space-time is considered. It is known that the end state of gravitational collapse, as to whether a black hole or a naked singularity is formed, depends on the mass function M(v, r). Here we give conditions for the mass function which correspond to the equation of the state P = αρ. where α ∈ (0, 1/3], and according to these conditions we obtain either a black hole or a naked singularity as the end state of gravitational collapse. We also give the conditions for the mass function under which the singularity is gravitationally strong. We present simple examples showing when the result of gravitational collapse is a naked singularity and when this singularity is strong. © 2016, Pleiades Publishing, Ltd. Source


Gavrilov S.P.,Herzen State Pedagogical University | Gitman D.M.,Sao Paulo State University
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2016

Using a quantum field theory approach, we consider particle scattering and vacuum instability in the so-called L-constant electric field, which is a constant electric field confined between two capacitor plates separated by a finite distance L. We obtain and analyze special sets of stationary solutions of the Dirac and Klein-Gordon equations with the L-constant electric field. Then, we represent probabilities of particle scattering and characteristics of the vacuum instability (related to pair creation) in terms of the introduced solutions. From exact formulas, we derive asymptotic expressions for the differential mean numbers, for the total mean number of created particles, and for the vacuum-to-vacuum transition probability. Using the equivalence principle, we demonstrate that the distributions of particles created by the L-constant electric field and the gravitational field of a black hole have a similar thermal structure. © 2016 American Physical Society. Source


Vertogradov V.D.,Herzen State Pedagogical University
Gravitation and Cosmology | Year: 2015

According to Penrose’s effect, particles with negative energy can exist in the ergospheres of rotating black holes. We analyze geodesics for such particles and show that there are no circular and elliptic orbits in the ergosphere of a rotating black hole. We also show that there are geodesics which begin and terminate at the singularity and present the conditions under which such geodesics do not begin and terminate at the singularity. © 2015, Pleiades Publishing, Ltd. Source


Gavrilov S.P.,Herzen State Pedagogical University | Gitman D.M.,Sao Paulo State University
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2016

QED with strong external backgrounds that can create particles from the vacuum is well developed for the so-called t-electric potential steps, which are time-dependent external electric fields that are switched on and off at some time instants. However, there exist many physically interesting situations where external backgrounds do not switch off at the time infinity. E.g., these are time-independent nonuniform electric fields that are concentrated in restricted space areas. The latter backgrounds represent a kind of spatial x-electric potential steps for charged particles. They can also create particles from the vacuum, the Klein paradox being closely related to this process. Approaches elaborated for treating quantum effects in the t-electric potential steps are not directly applicable to the x-electric potential steps and their generalization for x-electric potential steps was not sufficiently developed. We believe that the present work represents a consistent solution of the latter problem. We have considered a canonical quantization of the Dirac and scalar fields with x-electric potential step and have found in- and out-creation and annihilation operators that allow one to have particle interpretation of the physical system under consideration. To identify in- and out-operators we have performed a detailed mathematical and physical analysis of solutions of the relativistic wave equations with an x-electric potential step with subsequent QFT analysis of correctness of such an identification. We elaborated a nonperturbative (in the external field) technique that allows one to calculate all characteristics of zero-order processes, such, for example, scattering, reflection, and electron-positron pair creation, without radiation corrections, and also to calculate Feynman diagrams that describe all characteristics of processes with interaction between the in-, out-particles and photons. These diagrams have formally the usual form, but contain special propagators. Expressions for these propagators in terms of in- and out-solutions are presented. We apply the elaborated approach to two popular exactly solvable cases of x-electric potential steps, namely, to the Sauter potential and to the Klein step. © 2016 American Physical Society. Source


Gavrilov S.P.,Herzen State Pedagogical University | Gitman D.M.,Sao Paulo State University | Shishmarev A.A.,University of Sao Paulo
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2015

We study statistical properties of states of massive quantized charged Dirac and Klein-Gordon fields interacting with a background that violates the vacuum stability, first in general terms and then for a special electromagnetic background. As a starting point, we use a nonperturbative expression for the density operators of such fields derived by Gavrilov et al. [Gavrilov, Gitman, and Tomazelli, Nucl. Phys. B 795, 645 (2008)NUPBBO0550-321310.1016/j.nuclphysb.2007.11.029]. We construct the reduced density operators for electron and positron subsystems and discuss a decoherence that may occur in the course of the evolution due to an intermediate measurement. By calculating the entropy we study the loss of the information in QED states due to partial reductions and a possible decoherence. We consider the so-called T-constant external electric field as an external background. This exactly solvable example allows us to calculate explicitly all statistical properties of various quantum states of the massive charged fields under consideration. © 2015 American Physical Society. Source

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