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.Comment: 17 pages; misprints corrected, misprints corrected, the title slightly changed during review process; version accepted for publicatio

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 $L$.Comment: 30 pages, 2 figures; misprints corrected, most of the auxiliary formulas are transferred to appendixes, version accepted for publication in PR

A note on "Measuring propagation speed of Coulomb fields" by R. de Sangro, G. Finocchiaro, P. Patteri, M. Piccolo, G. Pizzella

In connection with the discussion and the measurements fulfilled in [R. de Sangro et al., Eur. Phys. J. C 75 (2015) 137], the full identity is demonstrated between the Feynman formula for the field of a moving charge and the Lienard-Wiechert potentials.Comment: 3 pages. arXiv admin note: substantial text overlap with arXiv:1509.0640

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.Comment: 35 pages, 2 figures. misprints corrected, version accepted for publication in Phys. Rev. D. arXiv admin note: text overlap with arXiv:1511.02915, arXiv:1605.0907

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.Comment: 27 pages, 7 figures, some minor changes introduce

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 Li\'{e}nard-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.Comment: 12 page

Bound or free: interaction of the C-terminal domain of Escherichia coli single-stranded DNA-binding protein (SSB) with the tetrameric core of SSB.

Single-stranded DNA (ssDNA)-binding protein (SSB) protects ssDNA from degradation and recruits other proteins for DNA replication and repair. Escherichia coli SSB is the prototypical eubacterial SSB in a family of tetrameric SSBs. It consists of a structurally well-defined ssDNA binding domain (OB-domain) and a disordered C-terminal domain (C-domain). The eight-residue C-terminal segment of SSB (C-peptide) mediates the binding of SSB to many different SSB-binding proteins. Previously published nuclear magnetic resonance (NMR) data of the monomeric state at pH 3.4 showed that the C-peptide binds to the OB-domain at a site that overlaps with the ssDNA binding site, but investigating the protein at neutral pH is difficult because of the high molecular mass and limited solubility of the tetramer. Here we show that the C-domain is highly mobile in the SSB tetramer at neutral pH and that binding of the C-peptide to the OB-domain is so weak that most of the C-peptides are unbound even in the absence of ssDNA. We address the problem of determining intramolecular binding affinities in the situation of fast exchange between two states, one of which cannot be observed by NMR and cannot be fully populated. The results were confirmed by electron paramagnetic resonance spectroscopy and microscale thermophoresis. The C-peptide-OB-domain interaction is shown to be driven primarily by electrostatic interactions, so that binding of 1 equiv of (dT)35 releases practically all C-peptides from the OB-domain tetramer. The interaction is much more sensitive to NaCl than to potassium glutamate, which is the usual osmolyte in E. coli. As the C-peptide is predominantly in the unbound state irrespective of the presence of ssDNA, long-range electrostatic effects from the C-peptide may contribute more to regulating the activity of SSB than any engagement of the C-peptide by the OB-domain

Semiclassical description of undulator radiation

We present a semiclassical approximation for treating the radiation from classical currents. In particular, we present exact quantum states of the quantized electromagnetic field interacting with classical currents. These states are used to calculate a probability of many-photon radiation from the vacuum initial state of the electromagnetic field. In this manner, in the present article, we study characteristics of electromagnetic radiation of a planar undulator. We find the total radiated energy and its spectral-angular distribution. We compare our results with ones obtained in the framework of classical electrodynamics, discussing differences introduced by accurate accounting for the quantum nature of electromagnetic radiation and present results of some numerical calculations that confirm, in particular, the latter discussion. In Appendix we present the calculation of the radiated energy using an alternative parametrization of the trajectory of electrons moving in a planar undulator