7,915 research outputs found

### Semiclassical Inequivalence of Polygonalized Billiards

Polygonalization of any smooth billiard boundary can be carried out in
several ways. We show here that the semiclassical description depends on the
polygonalization process and the results can be inequivalent. We also establish
that generalized tangent-polygons are closest to the corresponding smooth
billiard and for de Broglie wavelengths larger than the average length of the
edges, the two are semiclassically equivalent.Comment: revtex, 4 ps figure

### Reconstructing vector bundles on curves from their direct image on symmetric powers

Let $C$ be an irreducible smooth complex projective curve, and let $E$ be an
algebraic vector bundle of rank $r$ on $C$. Associated to $E$, there are vector
bundles ${\mathcal F}_n(E)$ of rank $nr$ on $S^n(C)$, where $S^n(C)$ is n$-th symmetric power of$C$. We prove the following: Let$E_1$and$E_2$be
two semistable vector bundles on$C$, with${\rm genus}(C)\, \geq\, 2$. If${\mathcal F}_n(E_1)\,= \, {\mathcal F}_n(E_2)$for a fixed$n$, then$E_1
\,=\, E_2$

### Parameters and pitfalls in dark energy models with time varying equation of state

Are geometrical summaries of the CMB and LSS sufficient for estimating
cosmological parameters? And how does our choice of a dark energy model impact
the current constraints on standard cosmological parameters?
We address these questions in the context of the widely used CPL
parametrization of a time varying equation of state w in a cosmology allowing
spatial curvature. We study examples of different behavior allowed in a CPL
parametrization in a phase diagram, and relate these to effects on the
observables. We examine parameter constraints in such a cosmology by combining
WMAP5, SDSS, SNe, HST data sets by comparing the power spectra. We carefully
quantify the differences of these constraints to those obtained by using
geometrical summaries for the same data sets.
We find that (a) using summary parameters instead of the full data sets give
parameter constraints that are similar, but with discernible differences, (b)
due to degeneracies, the constraints on the standard parameters broaden
significantly for the same data sets. In particular, we find that in the
context of CPL dark energy, (i) a Harrison-Zeldovich spectrum cannot be ruled
out at $2\sigma$ levels with our current data sets. and (ii) the SNe IA, HST,
and WMAP 5 data are not sufficient to constrain spatial curvature; we
additionally require the SDSS DR4 data to achieve this.Comment: 20 pages, 11 figures, Submitted to Astrophysical Journa

### Anomaly in the electronic structure of a BCS superconductor, ZrB(12)

We investigate the electronic structure of a complex conventional
superconductor, ZrB12 employing high resolution photoemission spectroscopy and
ab initio band structure calculations. The experimental valence band spectra
could be described reasonably well within the local density approximation.
Energy bands close to the Fermi level possess t_(2g) symmetry and the Fermi
level is found to be in the proximity of quantum fluctuation regime. The
spectral lineshape in the high resolution spectra is complex exhibiting
signature of a deviation from Fermi liquid behavior. A dip at the Fermi level
emerges above the superconducting transition temperature that gradually grows
with the decrease in temperature. The spectral simulation of the dip and
spectral lineshape based on a phenomenological self energy suggests a finite
electron pair lifetime and a pseudogap above the superconducting transition
temperature.Comment: 8 figure

### Periodic Orbits in Polygonal Billiards

We review some properties of periodic orbit families in polygonal billiards
and discuss in particular a sum rule that they obey. In addition, we provide
algorithms to determine periodic orbit families and present numerical results
that shed new light on the proliferation law and its variation with the genus
of the invariant surface. Finally, we deal with correlations in the length
spectrum and find that long orbits display Poisson fluctuations.Comment: 30 pages (Latex) including 11 figure

### Sculpting the band gap: a computational approach

Materials with optimized band gap are needed in many specialized
applications. In this work, we demonstrate that Hellmann-Feynman forces
associated with the gap states can be used to find atomic coordinates with a
desired electronic density of states. Using tight-binding models, we show that
this approach can be used to arrive at electronically designed models of
amorphous silicon and carbon. We provide a simple recipe to include a priori
electronic information in the formation of computer models of materials, and
prove that this information may have profound structural consequences. An
additional example of a graphene nanoribbon is provided to demonstrate the
applicability of this approach to engineer 2-dimensional materials. The models
are validated with plane-wave density functional calculations.Comment: Submitted to Physical Review Letters on June 12, 201

### Can Inflation solve the Hierarchy Problem?

Inflation with tunneling from a false to a true vacuum becomes viable in the
presence of a scalar field that slows down the initial de Sitter phase. As a
by-product this field also sets dynamically the value of the Newton constant
observed today. This can be very large if the tunneling rate (which is
exponentially sensitive to the barrier) is small enough. Therefore along with
Inflation we also provide a natural dynamical explanation for why gravity is so
weak today. Moreover we predict a spectrum of gravity waves peaked at around
0.1 mHz, that will be detectable by the planned space inteferometer LISA.
Finally we discuss interesting predictions on cosmological scalar and tensor
fluctuations in the light the WMAP 3-year data.Comment: 7 pages. Replaced version with comparison with WMAP 3-year dat

### Equivariant vector bundles on complete symmetric varieties of minimal rank

Let $X$ be the wonderful compactification of a complex symmetric space $G/H$
of minimal rank. For a point $x\,\in\, G$, denote by $Z$ be the closure of
$BxH/H$ in $X$, where $B$ is a Borel subgroup of $G$. The universal cover of
$G$ is denoted by $\widetilde{G}$. Given a $\widetilde{G}$ equivariant vector
bundle $E$ on $X,$ we prove that $E$ is nef (respectively, ample) if and only
if its restriction to $Z$ is nef (respectively, ample). Similarly, $E$ is
trivial if and only if its restriction to $Z$ is so

### On equivariant principal bundles over wonderful compactifications

Let $G$ be a simple algebraic group of adjoint type over $\mathbb C$, and let
$M$ be the wonderful compactification of a symmetric space $G/H$. Take a
$\widetilde G$--equivariant principal $R$--bundle $E$ on $M$, where $R$ is a
complex reductive algebraic group and $\widetilde G$ is the universal cover of
$G$. If the action of the isotropy group $\widetilde H$ on the fiber of $E$ at
the identity coset is irreducible, then we prove that $E$ is polystable with
respect to any polarization on $M$. Further, for wonderful compactification of
the quotient of $\text{PSL}(n,{\mathbb C})$, $n\,\neq\, 4$ (respectively,
$\text{PSL}(2n,{\mathbb C})$, $n \geq 2$) by the normalizer of the projective
orthogonal group (respectively, the projective symplectic group), we prove that
the tangent bundle is stable with respect to any polarization on the wonderful
compactification

### The electron-phonon coupling is large for localized states

From density functional calculations, we show that localized states stemming
from defects or topological disorder exhibit an anomalously large
electron-phonon coupling. We provide a simple analysis to explain the
observation and perform a detailed study on an interesting system: amorphous
silicon. We compute first principles deformation potentials (by computing the
sensitivity of specific electronic eigenstates to individual classical normal
modes of vibration). We also probe thermal fluctuations in electronic
eigenvalues by first principles thermal simulation. We find a strong
correlation between a static property of the network [localization, as gauged
by inverse participation ratio (IPR)] and a dynamical property (the amplitude
of thermal fluctuations of electron energy eigenvalues) for localized electron
states. In particular, both the electron-phonon coupling and the variance of
energy eigenvalues are proportional to the IPR of the localized state. We
compare the results for amorphous Si to photoemission experiments. While the
computations are carried out for silicon, very similar effects have been seen
in other systems with disorder.Comment: 5 pages, 3 PostScript figure

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