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A. A. Shishmarev

Publications and source records attributed to A. A. Shishmarev.

9 recordsLinked to original sources
arXiv2021

Vacuum instability in time-dependent electric fields. New example of exactly solvable case

A new exactly solvable case in strong-field quantum electrodynamics with a time-dependent external electric field is presented. The corresponding field is given by an analytic function, which is asymmetric (in contrast to Sauter-like electric field) with respect to the time instant, where it reaches its maximum value, that is why we call it the analytic asymmetric electric field. We managed to exactly solve the Dirac equation with such a field, which made it possible to calculate characteristics of the corresponding vacuum instability nonperturbatively. We construct the so-called in- and out-solutions and with their help calculate mean differential and total numbers of created charged particles, probability of the vacuum to remain a vacuum, vacuum mean values of current density and energy-momentum tensor of the particles. We study the vacuum instability in regimes of rapidly and slowly changing analytic asymmetric electric field, and compare the obtained results with corresponding ones obtained earlier for the case of the symmetric Sauter-like electric field. We also compare exact results in the regime of slowly changing field with corresponding results obtained within the slowly varying field approximation recently proposed by two of the authors, thus demonstrating the effectiveness of such an approximation.

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arXiv2020

Quantum states of electromagnetic field interacting with a classical current and their applications to radiation problems

In the beginning, the synchrotron radiation (SR) was studied by classical methods using the Liénard-Wiechert potentials of electric currents. Subsequently, quantum corrections to the obtained classical formulas were studied, considering the emission of photons arising from electronic transitions between spectral levels, described in terms of the Dirac equation. In this paper, we consider an intermediate approach, in which electric currents generating the radiation are considered classically, whereas the quantum nature of the radiation is taken into account exactly. Such an approximate approach may be helpful in some cases, it allows one to study the one-photon and multi-photon radiation without complicating calculations using corresponding solutions of the Dirac equation. We construct exact quantum states of the electromagnetic field interacting with classical currents and study their properties. By their help, we calculate a probability of photon emission by classical currents and obtain relatively simple formulas for the one-photon and multi-photon radiation. Using the specific circular electric current, we calculate the corresponding SR. We discuss a relation of obtained results with known before, for example, with the Schott formula, with the Schwinger calculations, with one-photon radiation of scalar particles due to transitions between Landau levels, and with some previous results of calculating the two-photon SR.

hep-th↗
arXiv2019

States of charged quantum fields and their statistical properties in the presence of critical potential steps

Evolution of charged quantum fields under the action of constant nonuniform electric fields is studied. To this end we construct a special generating functional for density operators of the quantum fields with different initial conditions. Then we study some reductions of the density operators. For example, reductions to electron or positron subsystems, reduction induced by measurements, and spatial reduction to the left or to the right subsystems of final particles. We calculate von Neumann entropy for the corresponding reduced density operators, estimating in such a way an information loss. Then we illustrate the obtained results by calculations in a specific background of a strong constant electric field between two infinite capacitor plates separated by a finite distance $L$.

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arXiv2019

Pair production from the vacuum by a weakly inhomogeneous space-dependent electric potential step

There exists a clear physical motivation for theoretical studies of the vacuum instability related to the production of electron-positron pairs from a vacuum due to strong external electric fields. Various nonperturbative (with respect to the external fields) calculation methods were developed. Some of these methods are based on possible exact solutions of the Dirac equation. Unfortunately, there are only few cases when such solutions are known. Recently, an approximate but still nonperturbative approach to treat the vacuum instability caused by slowly varying $t$-electric potential steps (time dependent external fields that vanish as $|t|\rightarrow\infty$), which does not depend on the existence of the corresponding exact solutions, was formulated in Ref. [S. P. Gavrilov, D. M. Gitman, Phys. Rev. D \textbf{95}, 076013 (2017)]. Here, we present an approximate calculation method to treat nonperturbatively the vacuum instability in arbitrary weakly inhomogeneous $x$-electric potential steps (time-independent electric fields of a constant direction that are concentrated in restricted space areas, which means that the fields vanish as $|x|\rightarrow\infty$) in the absence of the corresponding exact solutions. Defining the weakly inhomogeneous regime in general terms, we demonstrate the universal character of the vacuum instability. This universality is associated with a large density of states excited from the vacuum by the electric field. Such a density appears in our approach as a large parameter. We derive universal representations for the total number and current density of the created particles. Relations of these representations with a locally constant field approximation for Schwinger's effective action are found.

hep-th↗
arXiv2017

Particle scattering and vacuum instability by exponential steps

Particle scattering and vacuum instability in a constant inhomogeneous electric field of particular peak configuration that consists of two (exponentially increasing and exponentially decreasing) independent parts are studied. It presents a new kind of external field where exact solutions of the Dirac and Klein-Gordon equations can be found. We obtain and analyze in- and out-solutions of the Dirac and Klein-Gordon equations in this configuration. By their help we calculate probabilities of particle scattering and characteristics of the vacuum instability. In particular, we consider in details three configurations: a smooth peak, a sharp peak, and a strongly asymmetric peak configuration. We find asymptotic expressions for total mean numbers of created particles and for vacuum-to-vacuum transition probability. We discuss a new regularization of the Klein step by the sharp peak and compare this regularization with another one given by the Sauter potential.

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arXiv2016

Moving point charge as a soliton in nonlinear electrodynamics

The field of a moving pointlike charge is determined in nonlinear local electrodynamics. As a model Lagrangian for the latter we take the one whose nonlinearity is the Euler-Heisenberg Lagrangian of quantum electrodynamics truncated at the leading term of its expansion in powers of the first field invariant. The total energy of the field produced by a point charge is finite in that model; thereby its field configuration is a soliton. We define a finite energy-momentum vector of this field configuration to demonstrate that its components satisfy the standard mechanical relation characteristic of a free moving massive particle.

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arXiv2016

Unitarity and vacuum deformation in QED with critical potential steps

The present article can be considered as a complement to the work P.R.D 93, 045002 (2016) where an nonperturbative approach to QED with x-electric critical potential steps was developed. In the beginning we study conditions when in- and out-spaces of the QED under consideration are unitarily equivalent. Then we construct a general density operator with the vacuum initial condition. Such an operator describes a deformation of the initial vacuum state by x-electric critical potential steps. We construct reductions of the deformed state to electron and positron subsystems, calculating the loss of the information in these reductions. We illustrate the general consideration studying the deformation of the quantum vacuum between two capacitor plates. Finally we calculate the entanglement measures of these reduced matrices as von Neumann entropies.

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arXiv2015

Statistical properties of states in QED with unstable vacuum

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 [S.P. Gavrilov, D.M. Gitman, and J.L. Tomazelli, Nucl. Phys. B 795, 645 (2008)]. 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. Next, 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.

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