8,665 research outputs found
Numerical modeling of troposphere-induced gravity wave propagation
Sources of internal gravity waves (IGW) in the upper atmosphere are assumed to be meteorological processes in the troposphere. These sources are vertically and horizontally inhomogeneous and time dependent. In order to describe the IGW propagation from such sources, a numerical solution of a system of hydrodynamical equations is required. In addition, it is necessary to take into account the influence of the altitude latitude inhomogeneity of the temperature and wind fields on the IGW propagation as well as the processes of dissipation. An algorithm is proposed for numerical modelling of the IGW propagation over a limited area from tropospheric local sources to the upper atmosphere. The algorithm takes into account all the above features. A spectral grid method is used with the expansion of wave fields into the Fourier series over longitude. The upper limit conditions were obtained from the requirement of a limited energy dissipation rate in an atmospheric column. The no slip (zero velocity) condition was used at the Earth's surface
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
On Quantization of Time-Dependent Systems with Constraints
The Dirac method of canonical quantization of theories with second class
constraints has to be modified if the constraints depend on time explicitly. A
solution of the problem was given by Gitman and Tyutin. In the present work we
propose an independent way to derive the rules of quantization for these
systems, starting from physical equivalent theory with trivial
non-stationarity.Comment: 4 page
Dirac equation in the magnetic-solenoid field
We consider the Dirac equation in the magnetic-solenoid field (the field of a
solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm
solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using
von Neumann's theory of deficiency indices. We find self-adjoint extensions of
the Dirac Hamiltonian in both above dimensions and boundary conditions at the
AB solenoid. Besides, for the first time, solutions of the Dirac equation in
the magnetic-solenoid field with a finite radius solenoid were found. We study
the structure of these solutions and their dependence on the behavior of the
magnetic field inside the solenoid. Then we exploit the latter solutions to
specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm
solenoid.Comment: 23 pages, 2 figures, LaTex fil
One-loop energy-momentum tensor in QED with electric-like background
We have obtained nonperturbative one-loop expressions for the mean
energy-momentum tensor and current density of Dirac's field on a constant
electric-like background. One of the goals of this calculation is to give a
consistent description of back-reaction in such a theory. Two cases of initial
states are considered: the vacuum state and the thermal equilibrium state.
First, we perform calculations for the vacuum initial state. In the obtained
expressions, we separate the contributions due to particle creation and vacuum
polarization. The latter contributions are related to the Heisenberg-Euler
Lagrangian. Then, we study the case of the thermal initial state. Here, we
separate the contributions due to particle creation, vacuum polarization, and
the contributions due to the work of the external field on the particles at the
initial state. All these contributions are studied in detail, in different
regimes of weak and strong fields and low and high temperatures. The obtained
results allow us to establish restrictions on the electric field and its
duration under which QED with a strong constant electric field is consistent.
Under such restrictions, one can neglect the back-reaction of particles created
by the electric field. Some of the obtained results generalize the calculations
of Heisenberg-Euler for energy density to the case of arbitrary strong electric
fields.Comment: 35 pages; misprints in the sign in definitions (40)-(43), and (68)
corrected, results unchange
Integration of D-dimensional 2-factor spaces cosmological models by reducing to the generalized Emden-Fowler equation
The D-dimensional cosmological model on the manifold describing the evolution of 2 Einsteinian factor spaces,
and , in the presence of multicomponent perfect fluid source is
considered. The barotropic equation of state for mass-energy densities and the
pressures of the components is assumed in each space. When the number of the
non Ricci-flat factor spaces and the number of the perfect fluid components are
both equal to 2, the Einstein equations for the model are reduced to the
generalized Emden-Fowler (second-order ordinary differential) equation, which
has been recently investigated by Zaitsev and Polyanin within discrete-group
analysis. Using the integrable classes of this equation one generates the
integrable cosmological models. The corresponding metrics are presented. The
method is demonstrated for the special model with Ricci-flat spaces
and the 2-component perfect fluid source.Comment: LaTeX file, no figure
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