3,131 research outputs found
The Canonical Function Method and its applications in Quantum Physics
The Canonical Function Method (CFM) is a powerful method that solves the
radial Schr\"{o}dinger equation for the eigenvalues directly without having to
evaluate the eigenfunctions. It is applied to various quantum mechanical
problems in Atomic and Molecular physics with presence of regular or singular
potentials. It has also been developed to handle single and multiple channel
scattering problems where the phaseshift is required for the evaluation of the
scattering cross-section. Its controllable accuracy makes it a valuable tool
for the evaluation of vibrational levels of cold molecules, a sensitive test of
Bohr correspondance principle and a powerful method to tackle local and
non-local spin dependent problems.Comment: 30 pages, 12 figures- To submit to Reviews of Modern Physic
General treatment of isocurvature perturbations and non-Gaussianities
We present a general formalism that provides a systematic computation of the
linear and non-linear perturbations for an arbitrary number of cosmological
fluids in the early Universe going through various transitions, in particular
the decay of some species (such as a curvaton or a modulus). Using this
formalism, we revisit the question of isocurvature non-Gaussianities in the
mixed inflaton-curvaton scenario and show that one can obtain significant
non-Gaussianities dominated by the isocurvature mode while satisfying the
present constraints on the isocurvature contribution in the observed power
spectrum. We also study two-curvaton scenarios, taking into account the
production of dark matter, and investigate in which cases significant
non-Gaussianities can be produced.Comment: Substantial improvements with respect to the first version. In
particular, we added a discussion on the confrontation of the models with
future observational data. This version is accepted for publication in JCA
Massive scalar states localized on a de Sitter brane
We consider a brane scenario with a massive scalar field in the
five-dimensional bulk. We study the scalar states that are localized on the
brane, which is assumed to be de Sitter. These localized scalar modes are
massive in general, their effective four-dimensional mass depending on the mass
of the five-dimensional scalar field, on the Hubble parameter in the brane and
on the coupling between the brane tension and the bulk scalar field. We then
introduce a purely four-dimensional approach based on an effective potential
for the projection of the scalar field in the brane, and discuss its regime of
validity. Finally, we explore the quasi-localized scalar states, which have a
non-zero width that quantifies their probability of tunneling from the brane
into the bulk.Comment: 14 pages; 5 figure
On the classification of normal G-varieties with spherical orbits
In this article, we investigate the geometry of reductive group actions on algebraic varieties. Given a connected reductive group , we elaborate on a geometric and combinatorial approach based on Luna-Vust theory to describe every normal -variety with spherical orbits. This description encompasses the classical case of spherical varieties and the theory of -varieties recently introduced by Altmann, Hausen, and S\"uss
Decomposition theorem and torus actions of complexity one
We algorithmically compute the intersection cohomology Betti numbers of any complete normal algebraic variety with a torus action of complexity one
On intersection cohomology with torus actions of complexity one
The purpose of this article is to investigate the intersection cohomology for algebraic varieties with torus action. Given
an algebraic torus T, one of our result determines the intersection cohomology Betti numbers of any normal projective T-variety admitting an algebraic curve as global quotient. The calculation is expressed in terms of a combinatorial description involving a divisorial fan which is the analogous of the defining fan of a toric variety. Our main tool to obtain this computation is a description of the decomposition theorem in this context
Quantization of scalar perturbations in brane-world inflation
We consider a quantization of scalar perturbations about a de Sitter brane in
a 5-dimensional anti-de Sitter (AdS) bulk spacetime. We first derive the second
order action for a master variable for 5-dimensional gravitational
perturbations. For a vacuum brane, there is a continuum of normalizable
Kaluza-Klein (KK) modes with . There is also a light radion mode with
which satisfies the junction conditions for two branes, but is
non-normalizable for a single brane model. We perform the quantization of these
bulk perturbations and calculate the effective energy density of the projected
Weyl tensor on the barne. If there is a test scalar field perturbation on the
brane, the mode together with the zero-mode and an infinite ladder
of discrete tachyonic modes become normalizable in a single brane model. This
infinite ladder of discrete modes as well as the continuum of KK modes with
introduce corrections to the scalar field perturbations at first-order
in a slow-roll expansion. We derive the second order action for the
Mukhanov-Sasaki variable coupled to the bulk perturbations which is needed to
perform the quantization and determine the amplitude of scalar perturbations
generated during inflation on the brane.Comment: 14 page
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