224 research outputs found
Spectral Asymptotics of Eigen-value Problems with Non-linear Dependence on the Spectral Parameter
We study asymptotic distribution of eigen-values of a quadratic
operator polynomial of the following form ,
where is a second order differential positive elliptic operator
with quadratic dependence on the spectral parameter . We derive
asymptotics of the spectral density in this problem and show how to compute
coefficients of its asymptotic expansion from coefficients of the asymptotic
expansion of the trace of the heat kernel of . The leading term in
the spectral asymptotics is the same as for a Laplacian in a cavity. The
results have a number of physical applications. We illustrate them by examples
of field equations in external stationary gravitational and gauge backgrounds.Comment: latex, 20 page
Resonant cavity photon creation via the dynamical Casimir effect
Motivated by a recent proposal for an experimental verification of the
dynamical Casimir effect, the macroscopic electromagnetic field within a
perfect cavity containing a thin slab with a time-dependent dielectric
permittivity is quantized in terms of the dual potentials. For the resonance
case, the number of photons created out of the vacuum due to the dynamical
Casimir effect is calculated for both polarizations (TE and TM). PACS:
42.50.Lc, 03.70.+k, 42.50.Dv, 42.60.Da.Comment: 4 pages, 1 figur
Vacuum Quantum Effects for Parallel Plates Moving by Uniform Acceleration in Static de Sitter Space
The Casimir forces on two parallel plates moving by uniform proper
acceleration in static de Sitter background due to conformally coupled massless
scalar field satisfying Dirichlet boundary conditions on the plates is
investigated. Static de Sitter space is conformally related to the Rindler
space, as a result we can obtain vacuum expectation values of energy-momentum
tensor for conformally invariant field in static de Sitter space from the
corresponding Rindler counterpart by the conformal transformation.Comment: 10 pages, no figures, accepted for publication in Int. J. Mod. Phys.
Restrictions on negative energy density in a curved spacetime
Recently a restriction ("quantum inequality-type relation") on the
(renormalized) energy density measured by a static observer in a "globally
static" (ultrastatic) spacetime has been formulated by Pfenning and Ford for
the minimally coupled scalar field, in the extension of quantum inequality-type
relation on flat spacetime of Ford and Roman. They found negative lower bounds
for the line integrals of energy density multiplied by a sampling (weighting)
function, and explicitly evaluate them for some specific spacetimes. In this
paper, we study the lower bound on spacetimes whose spacelike hypersurfaces are
compact and without boundary. In the short "sampling time" limit, the bound has
asymptotic expansion. Although the expansion can not be represented by locally
invariant quantities in general due to the nonlocal nature of the integral, we
explicitly evaluate the dominant terms in the limit in terms of the invariant
quantities. We also make an estimate for the bound in the long sampling time
limit.Comment: LaTex, 23 Page
Finite Temperature Casimir Effect and Dispersion in the Presence of Compactified Extra Dimensions
Finite temperature Casimir theory of the Dirichlet scalar field is developed,
assuming that there is a conventional Casimir setup in physical space with two
infinitely large plates separated by a gap R and in addition an arbitrary
number q of extra compacified dimensions. As a generalization of earlier
theory, we assume in the first part of the paper that there is a scalar
'refractive index' N filling the whole of the physical space region. After
presenting general expressions for free energy and Casimir forces we focus on
the low temperature case, as this is of main physical interest both for force
measurements and also for issues related to entropy and the Nernst theorem.
Thereafter, in the second part we analyze dispersive properties, assuming for
simplicity q=1, by taking into account dispersion associated with the first
Matsubara frequency only. The medium-induced contribution to the free energy,
and pressure, is calculated at low temperatures.Comment: 25 pages, one figure. Minor changes in the discussion. Version to
appear in Physica Script
Awaking the vacuum in relativistic stars
Void of any inherent structure in classical physics, the vacuum has revealed
to be incredibly crowded with all sorts of processes in relativistic quantum
physics. Yet, its direct effects are usually so subtle that its structure
remains almost as evasive as in classical physics. Here, in contrast, we report
on the discovery of a novel effect according to which the vacuum is compelled
to play an unexpected central role in an astrophysical context. We show that
the formation of relativistic stars may lead the vacuum energy density of a
quantum field to an exponential growth. The vacuum-driven evolution which would
then follow may lead to unexpected implications for astrophysics, while the
observation of stable neutron-star configurations may teach us much on the
field content of our Universe.Comment: To appear in Phys. Rev. Let
Reissner Nordstr\"{o}m Background Metric in Dynamical Co-ordinates: Exceptional Behaviour of Hadamard States
We cast the Reissner Nordstrom solution in a particular co-ordinate system
which shows dynamical evolution from initial data. The initial data for the
case is regular. This procedure enables us to treat the metric as a
collapse to a singularity. It also implies that one may assume Wald axioms to
be valid globally in the Cauchy development, especially when Hadamard states
are chosen. We can thus compare the semiclassical behaviour with spherical dust
case, looking upon the metric as well as state specific information as
evolution from initial data. We first recover the divergence on the Cauchy
horizon obtained earlier. We point out that the semiclassical domain extends
right upto the Cauchy horizon. This is different from the spherical dust case
where the quantum gravity domain sets in before. We also find that the
backreaction is not negligible near the central singularity, unlike the dust
case. Apart from these differences, the Reissner Nordstrom solution has a
similarity with dust in that it is stable over a considerable period of time.
The features appearing dust collapse mentioned above were suggested to be
generally applicable within spherical symmetry. Reissner Nordstrom background
(along with the quantum state) generated from initial data, is shown not to
reproduce them
Quantum Flux from a Moving Spherical Mirror
We calculate the flux from a spherical mirror which is expanding or
contracting with nearly uniform acceleration. We find that the flux at an
exterior point (which could in principle be a functional of the mirror's past
history) is actually found to be a local function, depending on the first and
second time derivatives of acceleration at the retarded time.Comment: 13 pages, 2 figures, RevTex, submitted to Phys. Rev.
Quantum Fields in an Expanding Universe
We extend our analysis for scalar fields in a Robertson-Walker metric to the
electromagnetic field and Dirac fields by the method of invariants. The issue
of the relation between conformal properties and particle production is
re-examined and it is verified that the electromagnetic and massless spinor
actions are conformal invariant, while the massless conformally coupled scalar
field is not. For the scalar field case it is pointed out that the violation of
conformal simmetry due to surface terms, although ininfluential for the
equation of motion, does lead to effects in the quantized theory.Comment: 15 pp, no figures, accepted for publication in Class. Quantum Gra
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