1,807 research outputs found
The Cauchy problems for Einstein metrics and parallel spinors
We show that in the analytic category, given a Riemannian metric on a
hypersurface and a symmetric tensor on , the metric
can be locally extended to a Riemannian Einstein metric on with second
fundamental form , provided that and satisfy the constraints on
imposed by the contracted Codazzi equations. We use this fact to study the
Cauchy problem for metrics with parallel spinors in the real analytic category
and give an affirmative answer to a question raised in B\"ar, Gauduchon,
Moroianu (2005). We also answer negatively the corresponding questions in the
smooth category.Comment: 28 pages; final versio
Health impact assessment and climate change: a scoping review
Climate change has various adverse impacts on public health, ranging from heat-related illness to an increased risk of undernutrition in low-income countries. Health impact assessment (HIA) has been advocated as a valuable tool to systematically identify and quantify the effects of climate change on public health and to inform and evaluate the impact of disease-specific adaptation measures as well as health co-benefits of mitigation measures. We conducted a scoping review to map out peer-reviewed literature on HIA in the context of climate change. Web of Science, Scopus and PubMed were searched without language or time restriction. Publications were included in the full text screening that presented or discussed the application of HIA for investigating health impacts of climate change, or associated adaptation and mitigation measures. In total, 76 peer-reviewed publications from 26 countries were included and characterized. There was a paucity of studies on HIA in the context of climate change from low- and middle-income countries. The most investigated climate change effects were related to temperature and air-pollution. Consequently, associated health impacts, such as respiratory or cardiovascular morbidity and mortality, were examined most frequently. Research-driven HIAs with a quantitative methodological approach were the predominant choice to assess health impacts of climate change. Only one in five publications applied a classical step-by-step HIA approach. While quantitative assessment of health impacts associated with climate change seems to be a well established field of research, the few publications applying a step-by-step HIA approach to systematically anticipate potential health impacts of climate change in a given context point at a missed opportunity for strengthening intersectoral collaboration to maximize health (co-) benefits of climate mitigation and adaptation measures. To promote the use of step-by-step HIA in regions that are most affected by climate change, HIA teaching and training efforts are urgently needed
Modulating motor learning through transcranial direct-current stimulation: An integrative view
Motor learning consists of the ability to improve motor actions through practice playing a major role in the acquisition of skills required for high-performance sports or motor function recovery after brain lesions. During the last decades, it has been reported that transcranial direct-current stimulation (tDCS), consisting in applying weak direct current through the scalp, is able of inducing polarity-specific changes in the excitability of cortical neurons. This low-cost, painless and well-tolerated portable technique has found a wide-spread use in the motor learning domain where it has been successfully applied to enhance motor learning in healthy individuals and for motor recovery after brain lesion as well as in pathological states associated to motor deficits. The main objective of this mini-review is to offer an integrative view about the potential use of tDCS for human motor learning modulation. Furthermore, we introduce the basic mechanisms underlying immediate and long-term effects associated to tDCS along with important considerations about its limitations and progression in recent years
Surgery and the spinorial tau-invariant
We associate to a compact spin manifold M a real-valued invariant \tau(M) by
taking the supremum over all conformal classes over the infimum inside each
conformal class of the first positive Dirac eigenvalue, normalized to volume 1.
This invariant is a spinorial analogue of Schoen's -constant, also
known as the smooth Yamabe number. We prove that if N is obtained from M by
surgery of codimension at least 2, then with . Various topological conclusions
can be drawn, in particular that \tau is a spin-bordism invariant below
. Below , the values of cannot accumulate from
above when varied over all manifolds of a fixed dimension.Comment: to appear in CPD
Experimental evidence for the role of cantori as barriers in a quantum system
We investigate the effect of cantori on momentum diffusion in a quantum
system. Ultracold caesium atoms are subjected to a specifically designed
periodically pulsed standing wave. A cantorus separates two chaotic regions of
the classical phase space. Diffusion through the cantorus is classically
predicted. Quantum diffusion is only significant when the classical phase-space
area escaping through the cantorus per period greatly exceeds Planck's
constant. Experimental data and a quantum analysis confirm that the cantori act
as barriers.Comment: 19 pages including 9 figures, Accepted for publication in Physical
Review E in March 199
A study of quantum decoherence in a system with Kolmogorov-Arnol'd-Moser tori
We present an experimental and numerical study of the effects of decoherence
on a quantum system whose classical analogue has Kolmogorov-Arnol'd-Moser (KAM)
tori in its phase space. Atoms are prepared in a caesium magneto-optical trap
at temperatures and densities which necessitate a quantum description. This
real quantum system is coupled to the environment via spontaneous emission. The
degree of coupling is varied and the effects of this coupling on the quantum
coherence of the system are studied. When the classical diffusion through a
partially broken torus is < hbar, diffusion of quantum particles is inhibited.
We find that increasing decoherence via spontaneous emission increases the
transport of quantum particles through the boundary.Comment: 19 pages including 6 figure
The Dirac operator on generalized Taub-NUT spaces
We find sufficient conditions for the absence of harmonic spinors on
spin manifolds constructed as cone bundles over a compact K\"ahler base. These
conditions are fulfilled for certain perturbations of the Euclidean metric, and
also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a
conjecture of Vi\csinescu and the second author.Comment: Final version, 16 page
Regularity for eigenfunctions of Schr\"odinger operators
We prove a regularity result in weighted Sobolev spaces (or
Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\"odinger operator.
More precisely, let K_{a}^{m}(\mathbb{R}^{3N}) be the weighted Sobolev space
obtained by blowing up the set of singular points of the Coulomb type potential
V(x) = \sum_{1 \le j \le N} \frac{b_j}{|x_j|} + \sum_{1 \le i < j \le N}
\frac{c_{ij}}{|x_i-x_j|}, x in \mathbb{R}^{3N}, b_j, c_{ij} in \mathbb{R}. If u
in L^2(\mathbb{R}^{3N}) satisfies (-\Delta + V) u = \lambda u in distribution
sense, then u belongs to K_{a}^{m} for all m \in \mathbb{Z}_+ and all a \le 0.
Our result extends to the case when b_j and c_{ij} are suitable bounded
functions on the blown-up space. In the single-electron, multi-nuclei case, we
obtain the same result for all a<3/2.Comment: to appear in Lett. Math. Phy
Quantum and classical chaos for a single trapped ion
In this paper we investigate the quantum and classical dynamics of a single
trapped ion subject to nonlinear kicks derived from a periodic sequence of
Guassian laser pulses. We show that the classical system exhibits diffusive
growth in the energy, or 'heating', while quantum mechanics suppresses this
heating. This system may be realized in current single trapped-ion experiments
with the addition of near-field optics to introduce tightly focussed laser
pulses into the trap.Comment: 8 pages, REVTEX, 8 figure
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