4,334 research outputs found
Gravitational Microlensing Near Caustics I: Folds
We study the local behavior of gravitational lensing near fold catastrophes.
Using a generic form for the lensing map near a fold, we determine the
observable properties of the lensed images, focusing on the case when the
individual images are unresolved, i.e., microlensing. Allowing for images not
associated with the fold, we derive analytic expressions for the photometric
and astrometric behavior near a generic fold caustic. We show how this form
reduces to the more familiar linear caustic, which lenses a nearby source into
two images which have equal magnification, opposite parity, and are equidistant
from the critical curve. In this case, the simplicity and high degree of
symmetry allows for the derivation of semi-analytic expressions for the
photometric and astrometric deviations in the presence of finite sources with
arbitrary surface brightness profiles. We use our results to derive some basic
properties of astrometric microlensing near folds, in particular we predict for
finite sources with uniform and limb darkening profiles, the detailed shape of
the astrometric curve as the source crosses a fold. We find that the
astrometric effects of limb darkening will be difficult to detect with the
currently planned accuracy of the Space Interferometry Mission. We verify our
results by numerically calculating the expected astrometric shift for the
photometrically well-covered Galactic binary lensing event OGLE-1999-BUL-23,
finding excellent agreement with our analytic expressions. Our results can be
applied to any lensing system with fold caustics, including Galactic binary
lenses and quasar microlensing.Comment: 37 pages, 7 figures. Revised version includes an expanded discussion
of applications. Accepted to ApJ, to appear in the August 1, 2002 issue
(v574
Distributional versions of Littlewood's Tauberian theorem
We provide several general versions of Littlewood's Tauberian theorem. These
versions are applicable to Laplace transforms of Schwartz distributions. We
apply these Tauberian results to deduce a number of Tauberian theorems for
power series where Ces\`{a}ro summability follows from Abel summability. We
also use our general results to give a new simple proof of the classical
Littlewood one-sided Tauberian theorem for power series.Comment: 15 page
A measure of majorisation emerging from single-shot statistical mechanics
The use of the von Neumann entropy in formulating the laws of thermodynamics
has recently been challenged. It is associated with the average work whereas
the work guaranteed to be extracted in any single run of an experiment is the
more interesting quantity in general. We show that an expression that
quantifies majorisation determines the optimal guaranteed work. We argue it
should therefore be the central quantity of statistical mechanics, rather than
the von Neumann entropy. In the limit of many identical and independent
subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered
but in the non-equilbrium regime the optimal guaranteed work can be radically
different to the optimal average. Moreover our measure of majorisation governs
which evolutions can be realized via thermal interactions, whereas the
nondecrease of the von Neumann entropy is not sufficiently restrictive. Our
results are inspired by single-shot information theory.Comment: 54 pages (15+39), 9 figures. Changed title / changed presentation,
same main results / added minor result on pure bipartite state entanglement
(appendix G) / near to published versio
Competing charge, spin, and superconducting orders in underdoped YBa2Cu3Oy
To explore the doping dependence of the recently discovered charge density
wave (CDW) order in YBa2Cu3Oy, we present a bulk-sensitive high-energy x-ray
study for several oxygen concentrations, including strongly underdoped
YBa2Cu3O6.44. Combined with previous data around the so-called 1/8 doping, we
show that bulk CDW order exists at least for hole concentrations (p) in the
CuO2 planes of 0.078 <~ p <~ 0.132. This implies that CDW order exists in close
vicinity to the quantum critical point for spin density wave (SDW) order. In
contrast to the pseudogap temperature T*, the onset temperature of CDW order
decreases with underdoping to T_CDW ~ 90K in YBa2Cu3O6.44. Together with a
weakened order parameter this suggests a competition between CDW and SDW
orders. In addition, the CDW order in YBa2Cu3O6.44 shows the same type of
competition with superconductivity as a function of temperature and magnetic
field as samples closer to p = 1/8. At low p the CDW incommensurability
continues the previously reported linear increasing trend with underdoping. In
the entire doping range the in-plane correlation length of the CDW order in
b-axis direction depends only very weakly on the hole concentration, and
appears independent of the type and correlation length of the oxygen-chain
order. The onset temperature of the CDW order is remarkably close to a
temperature T^\dagger that marks the maximum of 1/(T_1T) in planar 63^Cu
NQR/NMR experiments, potentially indicating a response of the spin dynamics to
the formation of the CDW. Our discussion of these findings includes a detailed
comparison to the charge stripe order in La2-xBaxCuO4.Comment: 11 pages, 5 figure
Genetic effects on longitudinal cognitive decline during the early stages of Alzheimer's disease
Cognitive decline in early-stage Alzheimer’s disease (AD) may depend on genetic variability. In the Swedish BioFINDER study, we used polygenic scores (PGS) (for AD, intelligence, and educational attainment) to predict longitudinal cognitive change (measured by mini-mental state examination (MMSE) [primary outcome] and other cognitive tests) over a mean of 4.2 years. We included 260 β-amyloid (Aβ) negative cognitively unimpaired (CU) individuals, 121 Aβ-positive CU (preclinical AD), 50 Aβ-negative mild cognitive impairment (MCI) patients, and 127 Aβ-positive MCI patients (prodromal AD). Statistical significance was determined at Bonferroni corrected p value < 0.05. The PGS for intelligence (beta = 0.1, p = 2.9e−02) was protective against decline in MMSE in CU and MCI participants regardless of Aβ status. The polygenic risk score for AD (beta = − 0.12, p = 9.4e−03) was correlated with the rate of change in MMSE and was partially mediated by Aβ-pathology (mediation effect 20%). There was no effect of education PGS on cognitive measures. Genetic variants associated with intelligence mitigate cognitive decline independent of Aβ-pathology, while effects of genetic variants associated with AD are partly mediated by Aβ-pathology
Toward semiclassical theory of quantum level correlations of generic chaotic systems
In the present work we study the two-point correlation function
of the quantum mechanical spectrum of a classically chaotic system. Recently
this quantity has been computed for chaotic and for disordered systems using
periodic orbit theory and field theory. In this work we present an independent
derivation, which is based on periodic orbit theory. The main ingredient in our
approach is the use of the spectral zeta function and its autocorrelation
function . The relation between and is
constructed by making use of a probabilistic reasoning similar to that which
has been used for the derivation of Hardy -- Littlewood conjecture. We then
convert the symmetry properties of the function into relations
between the so-called diagonal and the off-diagonal parts of . Our
results are valid for generic systems with broken time reversal symmetry, and
with non-commensurable periods of the periodic orbits.Comment: 15 pages(twocolumn format), LaTeX, EPSF, (figures included
Delayed - Choice Entanglement - Swapping with Vacuum-One Photon Quantum States
We report the experimental realization of a recently discovered quantum
information protocol by Asher Peres implying an apparent non-local quantum
mechanical retrodiction effect. The demonstration is carried out by applying a
novel quantum optical method by which each singlet entangled state is
physically implemented by a two-dimensional subspace of Fock states of a mode
of the electromagnetic field, specifically the space spanned by the vacuum and
the one photon state, along lines suggested recently by E. Knill et al., Nature
409, 46 (2001) and by M. Duan et al., Nature 414, 413 (2001). The successful
implementation of the new technique is expected to play an important role in
modern quantum information and communication and in EPR quantum non-locality
studies
Health Information Needs of the Pregnant Adolescent
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73151/1/j.1745-7599.1994.tb00906.x.pd
Distribution of Eigenvalues for the Modular Group
The two-point correlation function of energy levels for free motion on the
modular domain, both with periodic and Dirichlet boundary conditions, are
explicitly computed using a generalization of the Hardy-Littlewood method. It
is shown that ion the limit of small separations they show an uncorrelated
behaviour and agree with the Poisson distribution but they have prominent
number-theoretical oscillations at larger scale. The results agree well with
numerical simulations.Comment: 72 pages, Latex, the fiogures mentioned in the text are not vital,
but can be obtained upon request from the first Autho
Thermal Equation of State of Tantalum
We have investigated the thermal equation of state of tantalum from first
principles using the Linearized Augmented Plane Wave (LAPW) and pseudopotential
methods for pressures up to 300 GPa and temperatures up to 10000 K. The
equation of state at zero temperature was computed using LAPW. For finite
temperatures, mixed basis pseudopotential computations were performed for 54
atom supercells. The vibrational contributions were obtained by computing the
partition function using the particle in a cell model, and the the finite
temperature electronic free energy was obtained from the LAPW band structures.
We discuss the behavior of thermal equation of state parameters such as the
Gr\"uneisen parameter , , the thermal expansivity , the
Anderson-Gr\"uneisen parameter as functions of pressure and
temperature. The calculated Hugoniot shows excellent agreement with shock-wave
experiments. An electronic topological transition was found at approximately
200 GPa
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