88 research outputs found
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
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 -electric potential steps (time
dependent external fields that vanish as ), 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
-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 ) 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 .Comment: 30 pages, 2 figures; misprints corrected, most of the auxiliary
formulas are transferred to appendixes, version accepted for publication in
PR
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
The ice response to an oscillating load moving along a frozen channel
Unsteady response of an ice cover to an oscillating load moving along a frozen rectangular channel is studied for large times. The channel is filled with ideal incompressible fluid. The ice cover is modelled by a thin elastic plate. The flow caused by the deflection of the ice cover is potential. The problem is formulated within the linear theory of hydroelasticity. External load is modelled by a smooth localized pressure distribution. The load has periodic magnitude and moves along the channel with constant speed. Joint system of equations for the ice plate and the flow potential is closed by initial and boundary conditions: the ice plate is frozen to the walls of the channel, the flow velocity potential satisfies the impermeability condition at the rigid walls of the channel and linearized kinematic and dynamic conditions at the ice-liquid interface; at the initial time the load is stationary, the fluid in the channel is at rest and the stationary ice deflection is determined from the plate equation for the initial magnitude of the load. The problem is solved with the help of the Fourier transform along the channel. The ice deflection profile across the channel is sought in the form of the series of the eigenmodes of the ice cover oscillations in a channel. The solution of the problem is obtained in quadratures and consists of three parts: (1) symmetric with respect to the load deflection corresponding to the stationary load; (2) deflection corresponding to steady waves propagating at the load speed; (3) deflection corresponding to waves propagating from the load and caused by the oscillations of the load. The number of the last waves, depending on the parameters, can not exceed four for each eigenmode. In this article the results of the analytical and numerical analysis of the considered problem is presented
Deflection of ice cover caused by an underwater body moving in channel
Deflections and strains in an ice cover of a frozen channel caused by an underwater body moving under the ice with a constant speed along the channel are studied. The channel is of rectangular cross section, the fluid in the channel is inviscid and incompressible. The ice cover is clamped to the channel walls. The ice cover is modeled by a thin viscoelastic plate. The underwater body is modeled by a three-dimensional dipole. The intensity of the dipole is related to the speed and size of the underwater body. The problem is considered within the linear theory of hydroelasticity. For small deflections of the ice cover the velocity potential of the dipole in the channel is obtained by the method of images in leading order without account for the deflection of the ice cover. The problem of moving dipole in the channel with rigid walls provides the hydrodynamic pressure on the upper boundary of the channel, which corresponds to the ice cover. This pressure distribution does not depend on the deflection of the ice cover in the leading approximation. The deflections of the ice and strains in the ice plate are independent of time in the coordinate system moving together with the dipole. The problem is solved numerically using the Fourier transform, method of the normal modes and the truncation method for infinite systems of algebraic equations
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
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. [Gavrilov, Gitman, and 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. 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
- …