525 research outputs found
Legendrian Distributions with Applications to Poincar\'e Series
Let be a compact Kahler manifold and a quantizing holomorphic
Hermitian line bundle. To immersed Lagrangian submanifolds of
satisfying a Bohr-Sommerfeld condition we associate sequences , where is a
holomorphic section of . The terms in each sequence concentrate
on , and a sequence itself has a symbol which is a half-form,
, on . We prove estimates, as , of the norm
squares in terms of . More generally, we show that if and
are two Bohr-Sommerfeld Lagrangian submanifolds intersecting
cleanly, the inner products have an
asymptotic expansion as , the leading coefficient being an integral
over the intersection . Our construction is a
quantization scheme of Bohr-Sommerfeld Lagrangian submanifolds of . We prove
that the Poincar\'e series on hyperbolic surfaces are a particular case, and
therefore obtain estimates of their norms and inner products.Comment: 41 pages, LaTe
Crystal structure and chemistry of barium-graphite intercalation compounds
Graphite can accommodate various chemical species between graphene layers to form graphite intercalation compounds (GIC) [1]. Alkali metals can easily lead to bulk stage-1 intercalation compounds by vapor transport but for more electronegative elements, such as alkaline-earth metals or lanthanides, only a superficial intercalation is obtained and other synthesis methods have to be envisaged. Molten alloys, formed between an alkali metal and the targeted metal, have demonstrated their efficiency to prepare bulk and homogeneous GIC from these latter elements, for example the superconducting CaC6 phase [2], but some elements remain difficult to intercalate by this method. More recently, our team developed a method based on the work of Hagiwara et al., consisting in using a LiCl-KCl eutectic molten medium [3], which for example allowed to prepare for the first time a bulk SrC6 compound [4]. This work is focused on the intercalation of barium into graphite from the LiCl-KCl molten salts method. A bulk stage-1 BaC6 compound has been prepared and X-ray diffraction measurements confirmed its crystal structure [5]. Moreover, by varying the experimental conditions, two completely novel phases, denoted α and ÎČ, have been isolated. From ion beam analyses, Li0,2K0,6Ba0,35C6 and Li0,2K0,75Ba0,6C6 chemical formulae have been determined for α and ÎČ phases, respectively, showing that lithium and potassium are intercalated together with barium. X- ray diffraction led to the determination of the stacking sequence of each compound, and their planar unit cells. Lastly, a reaction mechanism is proposed, which explains the formation of the different phases observed in this study
An explicit formula for the Berezin star product
We prove an explicit formula of the Berezin star product on Kaehler
manifolds. The formula is expressed as a summation over certain strongly
connected digraphs. The proof relies on a combinatorial interpretation of
Englis' work on the asymptotic expansion of the Laplace integral.Comment: 19 pages, to appear in Lett. Math. Phy
General approach to the study of vacuum space-times with an isometry
In vacuum space-times the exterior derivative of a Killing vector field is a
2-form (named here as the Papapetrou field) that satisfies Maxwell's equations
without electromagnetic sources. In this paper, using the algebraic structure
of the Papapetrou field, we will set up a new formalism for the study of vacuum
space-times with an isometry, which is suitable to investigate the connections
between the isometry and the Petrov type of the space-time. This approach has
some advantages, among them, it leads to a new classification of these
space-times and the integrability conditions provide expressions that determine
completely the Weyl curvature. These facts make the formalism useful for
application to any problem or situation with an isometry and requiring the
knowledge of the curvature.Comment: 24 pages, LaTeX2e, IOP style. To appear in Classical and Quantum
Gravit
The Chevreton Tensor and Einstein-Maxwell Spacetimes Conformal to Einstein Spaces
In this paper we characterize the source-free Einstein-Maxwell spacetimes
which have a trace-free Chevreton tensor. We show that this is equivalent to
the Chevreton tensor being of pure-radiation type and that it restricts the
spacetimes to Petrov types \textbf{N} or \textbf{O}. We prove that the trace of
the Chevreton tensor is related to the Bach tensor and use this to find all
Einstein-Maxwell spacetimes with a zero cosmological constant that have a
vanishing Bach tensor. Among these spacetimes we then look for those which are
conformal to Einstein spaces. We find that the electromagnetic field and the
Weyl tensor must be aligned, and in the case that the electromagnetic field is
null, the spacetime must be conformally Ricci-flat and all such solutions are
known. In the non-null case, since the general solution is not known on closed
form, we settle with giving the integrability conditions in the general case,
but we do give new explicit examples of Einstein-Maxwell spacetimes that are
conformal to Einstein spaces, and we also find examples where the vanishing of
the Bach tensor does not imply that the spacetime is conformal to a -space.
The non-aligned Einstein-Maxwell spacetimes with vanishing Bach tensor are
conformally -spaces, but none of them are conformal to Einstein spaces.Comment: 22 pages. Corrected equation (12
Scalar fields on SL(2,R) and H^2 x R geometric spacetimes and linear perturbations
Using appropriate harmonics, we study the future asymptotic behavior of
massless scalar fields on a class of cosmological vacuum spacetimes. The
spatial manifold is assumed to be a circle bundle over a higher genus surface
with a locally homogeneous metric. Such a manifold corresponds to the
SL(2,R)-geometry (Bianchi VIII type) or the H^2 x R-geometry (Bianchi III
type). After a technical preparation including an introduction of suitable
harmonics for the circle-fibered Bianchi VIII to separate variables, we derive
systems of ordinary differential equations for the scalar field. We present
future asymptotic solutions for these equations in a special case, and find
that there is a close similarity with those on the circle-fibered Bianchi III
spacetime. We discuss implications of this similarity, especially to
(gravitational) linear perturbations. We also point out that this similarity
can be explained by the "fiber term dominated behavior" of the two models.Comment: 23 pages, no figures, to be published in Class. Quant. Gravi
Penrose Limits, the Colliding Plane Wave Problem and the Classical String Backgrounds
We show how the Szekeres form of the line element is naturally adapted to
study Penrose limits in classical string backgrounds. Relating the "old"
colliding wave problem to the Penrose limiting procedure as employed in string
theory we discuss how two orthogonal Penrose limits uniquely determine the
underlying target space when certain symmetry is imposed. We construct a
conformally deformed background with two distinct, yet exactly solvable in
terms of the string theory on R-R backgrounds, Penrose limits. Exploiting
further the similarities between the two problems we find that the Penrose
limit of the gauged WZW Nappi-Witten universe is itself a gauged WZW plane wave
solution of Sfetsos and Tseytlin. Finally, we discuss some issues related to
singularity, show the existence of a large class of non-Hausdorff solutions
with Killing Cauchy Horizons and indicate a possible resolution of the problem
of the definition of quantum vacuum in string theory on these time-dependent
backgrounds.Comment: Some misprints corrected. Matches the version in print. To appear in
Classical & Quantum Gravit
String theory and the Classical Stability of Plane Waves
The presence of fields with negative mass-squared typically leads to some
form of instability in standard field theories. The observation that, at least
in the light-cone gauge, strings propagating in plane wave spacetimes can have
worldsheet scalars with such tachyon-like masses suggests that the supergravity
background may itself be unstable. To address this issue, we perform a
perturbative analysis around the type IIB vacuum plane wave, the solution which
most obviously generates worldsheet scalars with negative mass-squared. We
argue that this background is perturbatively stable.Comment: 23 pages, no figures; v2: very minor changes, references added,
version accepted by PR
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