6,785 research outputs found
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
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
Proper time and path integral representations for the commutation function
On the example of the quantized spinor field, interacting with arbitrary
external electromagnetic field, the commutation function is studied. It is
shown that a proper time representation is available in any dimensions. Using
it, all the light cone singularities of the function are found explicitly,
generalizing the Fock formula in four dimensions, and a path integral
representation is constructed.Comment: 20 pages, LaTeX, uses pictex macro
Toda chains with type A_m Lie algebra for multidimensional m-component perfect fluid cosmology
We consider a D-dimensional cosmological model describing an evolution of
Ricci-flat factor spaces, M_1,...M_n (n > 2), in the presence of an m-component
perfect fluid source (n > m > 1). We find characteristic vectors, related to
the matter constants in the barotropic equations of state for fluid components
of all factor spaces.
We show that, in the case where we can interpret these vectors as the root
vectors of a Lie algebra of Cartan type A_m=sl(m+1,C), the model reduces to the
classical open m-body Toda chain.
Using an elegant technique by Anderson (J. Math. Phys. 37 (1996) 1349) for
solving this system, we integrate the Einstein equations for the model and
present the metric in a Kasner-like form.Comment: LaTeX, 2 ps figure
Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply
We consider unsteady heat transfer in a one-dimensional harmonic crystal
surrounded by a viscous environment and subjected to an external heat supply.
The basic equations for the crystal particles are stated in the form of a
system of stochastic differential equations. We perform a continualization
procedure and derive an infinite set of linear partial differential equations
for covariance variables. An exact analytic solution describing unsteady
ballistic heat transfer in the crystal is obtained. It is shown that the
stationary spatial profile of the kinetic temperature caused by a point source
of heat supply of constant intensity is described by the Macdonald function of
zero order. A comparison with the results obtained in the framework of the
classical heat equation is presented. We expect that the results obtained in
the paper can be verified by experiments with laser excitation of
low-dimensional nanostructures.Comment: 12 pages, 5 figure
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
Coherent and semiclassical states in magnetic field in the presence of the Aharonov-Bohm solenoid
A new approach to constructing coherent states (CS) and semiclassical states
(SS) in magnetic-solenoid field is proposed. The main idea is based on the fact
that the AB solenoid breaks the translational symmetry in the xy-plane, this
has a topological effect such that there appear two types of trajectories which
embrace and do not embrace the solenoid. Due to this fact, one has to construct
two different kinds of CS/SS, which correspond to such trajectories in the
semiclassical limit. Following this idea, we construct CS in two steps, first
the instantaneous CS (ICS) and the time dependent CS/SS as an evolution of the
ICS. The construction is realized for nonrelativistic and relativistic spinning
particles both in (2+1)- and (3+1)- dimensions and gives a non-trivial example
of SS/CS for systems with a nonquadratic Hamiltonian. It is stressed that CS
depending on their parameters (quantum numbers) describe both pure quantum and
semiclassical states. An analysis is represented that classifies parameters of
the CS in such respect. Such a classification is used for the semiclassical
decompositions of various physical quantities.Comment: 35 pages, 2 figures. Some typos in (77), (101), and (135) corrected
with respect to the published version. Results unchange
Quantum scalar field in FRW Universe with constant electromagnetic background
We discuss massive scalar field with conformal coupling in
Friedmann-Robertson-Walker (FRW) Universe of special type with constant
electromagnetic field. Treating an external gravitational-electromagnetic
background exactly, at first time the proper-time representations for out-in,
in-in, and out-out scalar Green functions are explicitly constructed as
proper-time integrals over the corresponding (complex) contours. The
vacuum-to-vacuum transition amplitudes and number of created particles are
found and vacuum instability is discussed. The mean values of the current and
energy-momentum tensor are evaluated, and different approximations for them are
investigated. The back reaction of the particles created to the electromagnetic
field is estimated in different regimes. The connection between proper-time
method and effective action is outlined. The effective action in scalar QED in
weakly-curved FRW Universe (De Sitter space) with weak constant electromagnetic
field is found as derivative expansion over curvature and electromagnetic field
strength. Possible further applications of the results are briefly mentioned.Comment: 38 pages, LaTe
Positive Expectancies and Subjective Well‑Being: A Prospective Study Among Undergraduates in Serbia
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