Hardcore dimer aspects of the SU(2) Singlet wavefunction

We demonstrate that any SU(2) singlet wavefunction can be characterized by a set of Valence Bond occupation numbers, testing dimer presence/vacancy on pairs of sites. This genuine quantum property of singlet states (i) shows that SU(2) singlets share some of the intuitive features of hardcore quantum dimers, (ii) gives rigorous basis for interesting albeit apparently ill-defined quantities introduced recently in the context of Quantum Magnetism or Quantum Information to measure respectively spin correlations and bipartite entanglement and, (iii) suggests a scheme to define consistently a wide family of quantities analogous to high order spin correlation. This result is demonstrated in the framework of a general functional mapping between the Hilbert space generated by an arbitrary number of spins and a set of algebraic functions found to be an efficient analytical tool for the description of quantum spins or qubits systems.Comment: 5 pages, 2 figure

The effect of social security payroll tax reductions on employment and wages: an evaluation of the 2003 French reform

public policy evaluation, payroll tax cuts, labour cost, semi-parametric estimations

Nonparametric estimator of the tail dependence coefficient: balancing bias and variance

A theoretical expression is derived for the mean squared error of a nonparametric estimator of the tail dependence coefficient, depending on a threshold that defines which rank delimits the tails of a distribution. We propose a new method to optimally select this threshold. It combines the theoretical mean squared error of the estimator with a parametric estimation of the copula linking observations in the tails. Using simulations, we compare this semiparametric method with other approaches proposed in the literature, including the plateau-finding algorithm

Local regularity for parabolic nonlocal operators

Weak solutions to parabolic integro-differential operators of order $\alpha \in (\alpha_0, 2)$ are studied. Local a priori estimates of H\"older norms and a weak Harnack inequality are proved. These results are robust with respect to $\alpha \nearrow 2$. In this sense, the presentation is an extension of Moser's result in 1971.Comment: 31 pages, 3 figure

Redox capacity of rocks and sediments by high temperature chalcometric titration

We present an analytical method to quantify the absolute redox capacity, ΔO2, of geological materials. The protocol consists in a high temperature chalcometric titration by which a known amount of oxygen gas is exchanged between a solid state oxygen donor, CuO, and an oxygen acceptor, the sample, at elevated temper- ature. Calibration of the method using elemental C, native S and magnetite demonstrates that it effectively oxidizes C, S and Fe to their terminal oxidation state, C4+, S6+ and Fe3+, respectively. Because the metric is independent of processes of internal equilibration within the system, it can be used for quantitative assessments of redox fluxes in open geological systems, in the surface or deep Earth. Preliminary results suggest that the mass specific redox capacity, dO2, of geological materials span many orders of magnitude, ranging from less than 500 μmol O2/g for ultramafic rocks and lower crustal amphibolites, to more than 30000 μmol O2/g for black shales. This highlights a counterintuitive yet fundamental characteristic of our planet. Rocks characterized by elevated dO2 values are ubiquitous in the oxic Earth’s surface, while the upper mantle and lower crust are typically composed of rocks with much lower dO2. This work will contribute to provide a more nuanced and complete perspective on the sedimentary and geodynamic processes that have shaped the redox structure of the Earth

Direct measurement of superluminal group velocity and of signal velocity in an optical fiber

We present an easy way of observing superluminal group velocities using a birefringent optical fiber and other standard devices. In the theoretical analysis, we show that the optical properties of the setup can be described using the notion of "weak value". The experiment shows that the group velocity can indeed exceed c in the fiber; and we report the first direct observation of the so-called "signal velocity", the speed at which information propagates and that cannot exceed c.Comment: 5 pages, 5 figure

Observables in Topological Yang-Mills Theories

Using topological Yang-Mills theory as example, we discuss the definition and determination of observables in topological field theories (of Witten-type) within the superspace formulation proposed by Horne. This approach to the equivariant cohomology leads to a set of bi-descent equations involving the BRST and supersymmetry operators as well as the exterior derivative. This allows us to determine superspace expressions for all observables, and thereby to recover the Donaldson-Witten polynomials when choosing a Wess-Zumino-type gauge.Comment: 39 pages, Late