The Cauchy problems for Einstein metrics and parallel spinors

We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W$, provided that $g$ and $W$ satisfy the constraints on $M$ 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 $\sigma$-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 $\tau(N) \geq \min\{\tau(M),\Lambda_n\}$ with $\Lambda_n>0$. Various topological conclusions can be drawn, in particular that \tau is a spin-bordism invariant below $\Lambda_n$. Below $\Lambda_n$, the values of $\tau$ 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 $L^2$ 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