8,396 research outputs found
The CWKB approach to non-reflecting potential and cosmological implications
We discuss the method of calculating the reflection coefficient using complex
trajectory WKB (CWKB) approximation. This enables us to give an interpretation
of non-reflecting nature of the potential under certain conditions and clarify
some points, reported incorrectly elsewhere [vs:ejp] for the potential
. We show that the repeated reflectios between the
turning points are essential, which most authors overlooked, in obtaining the
non-reflecting c ondition. We find that the considered repeated reflection
paths are in conformity with Bogolubov transformation technique. We discuss the
implications of the results when applied to the particle production scenario,
considering as a time variable and also stress the cosmological
implications of the result with reference to radiation domonated and de Sitter
spacetime.Comment: 9 pages, late
On bouncing solutions in non-local gravity
A non-local modified gravity model with an analytic function of the
d'Alembert operator is considered. This model has been recently proposed as a
possible way of resolving the singularities problem in cosmology. We present an
exact bouncing solution, which is simpler compared to the already known one in
this model in the sense it does not require an additional matter to satisfy all
the gravitational equations.Comment: 5 pages; v2: matching the jounral versio
The Topology of Parabolic Character Varieties of Free Groups
Let G be a complex affine algebraic reductive group, and let K be a maximal
compact subgroup of G. Fix elements h_1,...,h_m in K. For n greater than or
equal to 0, let X (respectively, Y) be the space of equivalence classes of
representations of the free group of m+n generators in G (respectively, K) such
that for each i between 1 and m, the image of the i-th free generator is
conjugate to h_i. These spaces are parabolic analogues of character varieties
of free groups. We prove that Y is a strong deformation retraction of X. In
particular, X and Y are homotopy equivalent. We also describe explicit examples
relating X to relative character varieties.Comment: 16 pages, version 2 includes minor revisions and some modified
proofs, accepted for publication in Geometriae Dedicat
The CWKB Method of Particle Production in Periodic Potential
In this work we study the particle production in time dependent periodic
potential using the method of complex time WKB (CWKB) approximation. In the
inflationary cosmology at the end of inflationary stage, the potential becomes
time dependent as well as periodic. Reheating occurs due to particle production
by the oscillating inflaton field. Using CWKB we obtain almost identical
results on catastrophic particle production as obtained by others.Comment: 17 pages, latex, 2 figure
Nonlocal Gravitational Models and Exact Solutions
A nonlocal gravity model with a function , where is
the d'Alembert operator, is considered. The algorithm, allowing to reconstruct
, corresponding to the given Hubble parameter and the state
parameter of the matter, is proposed. Using this algorithm, we find the
functions , corresponding to de Sitter solutions.Comment: 5 pages, v2: refs. added, to appear in the proceedings of the
International Workshop "Supersymmetries and Quantum Symmetries" (SQS'2011),
Dubna, Russia, July 18-23, 2011, http://theor.jinr.ru/sqs/2011
Direct images of bundles under Frobenius morphisms
Let be a smooth projective variety of dimension over an algebraically
closed field with and be the relative
Frobenius morphism. For any vector bundle on , we prove that instability
of is bounded by instability of
()(Corollary \ref{cor3.8}). When is a smooth
projective curve of genus , it implies being stable whenever
is stable.Comment: the final version to appear in Invent. math. (2008
Magnetocaloric properties of nanocrystalline LaCaMnO
Some recent experimental studies show the invisibility of antiferromagnetic
transition in the cases of manganites when their particle size is reduced to
nanometer scale. In complete contrast to these cases, we have observed the
signature of antiferromagnetic transition in the magnetocaloric properties of
nanocrystalline LaCaMnO of average particle size 70
and 60 nm similar to its polycrystalline bulk form. The system exhibit inverse
magnetocaloric effect in its polycrystalline and nanocrystalline form. An extra
ferromagnetic phase is stabilized at low temperature for the sample with
particle size nm.Comment: 3 Figure
Higgs bundles and fundamental group schemes
Relying on a notion of ``numerical effectiveness'' for Higgs bundles, we show that the category of ``numerically flat'' Higgs vector bundles on a smooth projective variety is a Tannakian category. We introduce the associated group scheme, that we call the ``Higgs fundamental group scheme of ,'' and show that its properties are related to a conjecture about the vanishing of the Chern classes of numerically flat Higgs vector bundles
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