558 research outputs found
The Casimir effect for thin plasma sheets and the role of the surface plasmons
We consider the Casimir force betweeen two dielectric bodies described by the
plasma model and between two infinitely thin plasma sheets. In both cases in
addition to the photon modes surface plasmons are present in the spectrum of
the electromagnetic field. We investigate the contribution of both types of
modes to the Casimir force and confirm resp. find in both models large
compensations between the plasmon modes themselves and between them and the
photon modes especially at large distances. Our conclusion is that the
separation of the vacuum energy into plasmon and photon contributions must be
handled with care except for the case of small separations.Comment: submitted to JPhysA Special Issue QFEXT'05, replaced due to a wrong
Latex comman
Investigation of dynamical systems using tools of the theory of invariants and projective geometry
The investigation of nonlinear dynamical systems of the type
by means of reduction to
some ordinary differential equations of the second order in the form
is done. The main
backbone of this investigation was provided by the theory of invariants
developed by S. Lie, R. Liouville and A. Tresse at the end of the 19th century
and the projective geometry of E. Cartan. In our work two, in some sense
supplementary, systems are considered: the Lorenz system and the R\"o\ss ler system
. The invarinats for the ordinary
differential equations, which correspond to the systems mentioned abouve, are
evaluated. The connection of values of the invariants with characteristics of
dynamical systems is established.Comment: 18 pages, Latex, to appear in J. of Applied Mathematics (ZAMP
Vacuum energy in the presence of a magnetic string with delta function profile
We present a calculation of the ground state energy of massive spinor fields
and massive scalar fields in the background of an inhomogeneous magnetic string
with potential given by a delta function. The zeta functional regularization is
used and the lowest heat kernel coefficients are calculated. The rest of the
analytical calculation adopts the Jost function formalism. In the numerical
part of the work the renormalized vacuum energy as a function of the radius
of the string is calculated and plotted for various values of the strength of
the potential. The sign of the energy is found to change with the radius. For
both scalar and spinor fields the renormalized energy shows no logarithmic
behaviour in the limit , as was expected from the vanishing of the heat
kernel coefficient , which is not zero for other types of profiles.Comment: 30 pages, 10 figure
Heat Kernel Expansion for Semitransparent Boundaries
We study the heat kernel for an operator of Laplace type with a
-function potential concentrated on a closed surface. We derive the
general form of the small asymptotics and calculate explicitly several
first heat kernel coefficients.Comment: 16 page
Ground state energy in a wormhole space-time
The ground state energy of the massive scalar field with non-conformal
coupling on the short-throat flat-space wormhole background is calculated
by using zeta renormalization approach. We discuss the renormalization and
relevant heat kernel coefficients in detail. We show that the stable
configuration of wormholes can exist for . In particular case of
massive conformal scalar field with , the radius of throat of stable
wormhole . The self-consistent wormhole has radius of throat
and mass of scalar boson ( and
are the Planck length and mass, respectively).Comment: revtex, 18 pages, 3 eps figures. accepted in Phys.Rev.
The ground state energy of a spinor field in the background of a finite radius flux tube
We develop a formalism for the calculation of the ground state energy of a
spinor field in the background of a cylindrically symmetric magnetic field. The
energy is expressed in terms of the Jost function of the associated scattering
problem. Uniform asymptotic expansions needed are obtained from the
Lippmann-Schwinger equation. The general results derived are applied to the
background of a finite radius flux tube with a homogeneous magnetic field
inside and the ground state energy is calculated numerically as a function of
the radius and the flux. It turns out to be negative, remaining smaller by a
factor of than the classical energy of the background except for very
small values of the radius which are outside the range of applicability of QED.Comment: 25 pages, 3 figure
Dynamical Casimir Effect in a one-dimensional uniformly contracting cavity
We consider particle creation (the Dynamical Casimir effect) in a uniformly
contracting ideal one-dimensional cavity non-perturbatively. The exact
expression for the energy spectrum of created particles is obtained and its
dependence on parameters of the problem is discussed. Unexpectedly, the number
of created particles depends on the duration of the cavity contracting
non-monotonously. This is explained by quantum interference of the events of
particle creation which are taking place only at the moments of acceleration
and deceleration of a boundary, while stable particle states exist (and thus no
particles are created) at the time of contracting.Comment: 13 pages, 4 figure
Long range chromomagnetic fields at high temperature
The magnetic mass of neutral gluons in Abelian chromomagnetic field at high
temperature is calculated in SU(2)$ gluodynamics. It is noted that such type
fields are spontaneously generated at high temperature. The mass is computed
either from the Schwinger-Dyson equation accounting for the one-loop
polarization tensor or in Monte-Carlo simulations on a lattice. In latter case,
an average magnetic flux penetrating a plaquette is measured for a number of
lattices. Both calculations are in agreement with each other and result in zero
magnetic mass. Some applications of the results obtained are discussed.Comment: 14 pages, 1 figur
Casimir energy in the Fulling--Rindler vacuum
The Casimir energy is evaluated for massless scalar fields under Dirichlet or
Neumann boundary conditions, and for the electromagnetic field with perfect
conductor boundary conditions on one and two infinite parallel plates moving by
uniform proper acceleration through the Fulling--Rindler vacuum in an arbitrary
number of spacetime dimension. For the geometry of a single plate the both
regions of the right Rindler wedge, (i) on the right (RR region) and (ii) on
the left (RL region) of the plate are considered. The zeta function technique
is used, in combination with contour integral representations. The Casimir
energies for separate RR and RL regions contain pole and finite contributions.
For an infinitely thin plate taking RR and RL regions together, in odd spatial
dimensions the pole parts cancel and the Casimir energy for the whole Rindler
wedge is finite. In spatial dimensions the total Casimir energy for a
single plate is negative for Dirichlet scalar and positive for Neumann scalar
and the electromagnetic field. The total Casimir energy for two plates geometry
is presented in the form of a sum of the Casimir energies for separate plates
plus an additional interference term. The latter is negative for all values of
the plates separation for both Dirichlet and Neumann scalars, and for the
electromagnetic field.Comment: 28 pages, 4 figures, references added, typos corrected, accepted for
publication in Phys. Rev.
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