30 research outputs found
Field equations and vector order parameter in braneworld applications
Phase transitions with spontaneous symmetry breaking and vector order
parameter are considered in multidimensional theory of general relativity.
Covariant equations, describing the gravitational properties of topological
defects, are derived. The topological defects are classified in accordance with
the symmetry of the covariant derivative of the vector order parameter. The
abilities of the derived equations are demonstrated in application to the brane
world concept. New solutions of the Einstein equations with a transverse vector
order parameter are presented. In the vicinity of phase transition the
solutions are found analytically. Comparison with the commonly used scalar
multiplet approach demonstrates the advantages of the vector order parameter.Comment: Text of the plenary report by B.E.Meierovich at the International
Conference "Modern problems of gravitation, cosmology, and relativistic
astrophysics", Moscow, June 27 -- July 3, 2010 (RUDN-10
Global Monopole in General Relativity
We consider the gravitational properties of a global monopole on the basis of
the simplest Higgs scalar triplet model in general relativity. We begin with
establishing some common features of hedgehog-type solutions with a regular
center, independent of the choice of the symmetry-breaking potential. There are
six types of qualitative behavior of the solutions; we show, in particular,
that the metric can contain at most one simple horizon. For the standard
Mexican hat potential, the previously known properties of the solutions are
confirmed and some new results are obtained. Thus, we show analytically that
solutions with monotonically growing Higgs field and finite energy in the
static region exist only in the interval , being the
squared energy of spontaneous symmetry breaking in Planck units. The
cosmological properties of these globally regular solutions apparently favor
the idea that the standard Big Bang might be replaced with a nonsingular static
core and a horizon appearing as a result of some symmetry-breaking phase
transition on the Planck energy scale. In addition to the monotonic solutions,
we present and analyze a sequence of families of new solutions with oscillating
Higgs field. These families are parametrized by , the number of knots of the
Higgs field, and exist for ; all such
solutions possess a horizon and a singularity beyond it.Comment: 14 pages, 8 figure
Spontaneous Symmetry Breaking in General Relativity. Vector Order Parameter
Gravitational properties of a hedge-hog type topological defect in two extra
dimensions are considered in General Relativity employing a vector as the order
parameter. All previous considerations were done using the order parameter in
the form of a multiplet in a target space of scalar fields. The difference of
these two approaches is analyzed and demonstrated in detail. Regular solutions
of the Einstein equations are studied analytically and numerically. It is shown
that the existence of a negative cosmological constant is sufficient for the
spontaneous symmetry breaking of the initially plain bulk. Regular
configurations have a growing gravitational potential and are able to trap the
matter on the brane. If the energy of spontaneous symmetry breaking is high,
the gravitational potential has several points of minimum. Identical in the
uniform bulk spin-less particles, being trapped within separate minima, acquire
different masses and appear to the observer on brane as different particles
with integer spins.Comment: 23 pages, 6 figure
Gravitating global monopoles in extra dimensions and the brane world concept
Multidimensional configurations with Minkowski external space-time and a
spherical global monopole in extra dimensions are discussed in the context of
the brane world concept. The monopole is formed with a hedgehog-like set of
scalar fields \phi^i with a symmetry-breaking potential V depending on the
magnitude \phi^2 = \phi^i \phi^i. All possible kinds of globally regular
configurations are singled out without specifying the shape of V(\phi). These
variants are governed by the maximum value \phi_m of the scalar field,
characterizing the energy scale of symmetry breaking. If \phi_m < \phi_cr
(where \phi_cr is a critical value of \phi related to the multidimensional
Planck scale), the monopole reaches infinite radii while in the ``strong field
regime'', when \phi_m\geq \phi_cr, the monopole may end with a cylinder of
finite radius or possess two regular centers. The warp factors of monopoles
with both infinite and finite radii may either exponentially grow or tend to
finite constant values far from the center. All such configurations are shown
to be able to trap test scalar matter, in striking contrast to RS2 type 5D
models. The monopole structures obtained analytically are also found
numerically for the Mexican hat potential with an additional parameter acting
as a cosmological constant.Comment: 21 pages, 6 figures, latex, gc styl
Formation of bound states of electrons in spherically symmetric oscillations of plasma
We study spherically symmetric oscillations of electrons in plasma in the
frame of classical electrodynamics. Firstly, we analyze the electromagnetic
potentials for the system of radially oscillating charged particles. Secondly,
we consider both free and forced spherically symmetric oscillations of
electrons. Finally, we discuss the interaction between radially oscillating
electrons through the exchange of ion acoustic waves. It is obtained that the
effective potential of this interaction can be attractive and can transcend the
Debye-Huckel potential. We suggest that oscillating electrons can form bound
states at the initial stages of the spherical plasma structure evolution. The
possible applications of the obtained results for the theory of natural
plasmoids are examined.Comment: 9 pages in LaTeX2e, no figures; paper was significantly modified, 2
new references added, some inessential mathematics was removed, many typos
were corrected; final variant to be published in Physica Script
Pairing of charged particles in a quantum plasmoid
We study a quantum spherically symmetric object which is based on radial
plasma oscillations. Such a plasmoid is supposed to exist in a dense plasma
containing electrons, ions, and neutral particles. The method of creation and
annihilation operators is applied to quantize the motion of charged particles
in a self-consistent potential. We also study the effective interaction between
oscillating particles owing to the exchange of a virtual acoustic wave, which
is excited in the neutral component of plasma. It is shown that this
interaction can be attractive and result in the formation of ion pairs. We
discuss possible applications of this phenomenon in astrophysical and
terrestrial plasmas.Comment: 17 pages, no figures, two columns, LaTeX2e; paper was significantly
revised; title was changed; 16 new references were included; the discussion
on ion-acoustic waves was added to Sec. 2; Secs. 3 and 4 were shortened; a
more detailed discussion was added to Sec. 7; accepted for publication to
J.Phys.
Landau damping and anomalous skin effect in low-pressure gas discharges: Self-consistent treatment of collisionless heating
In low-pressure discharges, where the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially nonlocal. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the nonlocal conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, nonuniform, nearly collisionless plasmas of low-pressure discharges is reported. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. This system was applied to the calculation of collisionless heating in capacitively and inductively coupled plasmas. In particular, the importance of accounting for the nonuniform plasma density profile for computing the current density profile and the EEDF is demonstrated. The enhancement of collisionless heating due to the bounce resonance between the electron motion in the potential well and the external radio-frequency electric field is investigated. It is shown that a nonlinear and self-consistent treatment is necessary for the correct description of collisionless heating