9,510 research outputs found
Effective energy-momentum tensor of strong-field QED with unstable vacuum
We study the influence of a vacuum instability on the effective
energy-momentum tensor (EMT) of QED, in the presence of a quasiconstant
external electric field, by means of the relevant Green functions. In the case
when the initial vacuum, |0,in>, differs essentially from the final vacuum,
|0,out>, we find explicitly and compared both the vacuum average value of EMT,
, and the matrix element, . In
the course of the calculation we solve the problem of the special divergences
connected with infinite time T of acting of the constant electric field. The
EMT of pair created by an electric field from the initial vacuum is presented.
The relations of the obtained expressions to the Euler-Heisenberg's effective
action are established.Comment: 8 pages, 1 figure, Talk given at "QFEXT'05", the 7-th workshop on
quantum field theory under the influence of external conditions, Barcelona,
Spain, Sept. 5-9, 2005; minor misprints correcte
On the explicit solutions of the elliptic Calogero system
Let be the coordinates of particles on the circle,
interacting with the integrable potential , where
is the Weierstrass elliptic function. We show that every symmetric
elliptic function in is a meromorphic function in time. We
give explicit formulae for these functions in terms of genus theta
functions.Comment: 18 pages, Late
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
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
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
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