Weyl laws for partially open quantum maps

We study a toy model for "partially open" wave-mechanical system, like for instance a dielectric micro-cavity, in the semiclassical limit where ray dynamics is applicable. Our model is a quantized map on the 2-dimensional torus, with an additional damping at each time step, resulting in a subunitary propagator, or "damped quantum map". We obtain analogues of Weyl's laws for such maps in the semiclassical limit, and draw some more precise estimates when the classical dynamic is chaotic.Comment: 35 pages, 5 figures. Corrected typos. Some proofs clarifie

Exponential stabilization without geometric control

We present examples of exponential stabilization for the damped wave equation on a compact manifold in situations where the geometric control condition is not satisfied. This follows from a dynamical argument involving a topological pressure on a suitable uncontrolled set

Resonances near the real axis for manifolds with hyperbolic trapped sets

For manifolds Euclidian at infinity and compact perturbations of the Laplacian, we show that under assumptions involving hyperbolicity of the classical flow on the trapped set and its period spectrum, there are strips below the real axis where the resonance counting function grows sub-linearly. We also provide an inverse result, showing that the knowledge of the scattering poles can give some information about the Hausdorff dimension of the trapped set when the classical flow satisfies the Axiom-A condition

From resolvent estimates to damped waves

In this paper we show how to obtain decay estimates for the damped wave equation on a compact manifold without geometric control via knowledge of the dynamics near the un-damped set. We show that if replacing the damping term with a higher-order \emph{complex absorbing potential} gives an operator enjoying polynomial resolvent bounds on the real axis, then the "resolvent" associated to our damped problem enjoys bounds of the same order. It is known that the necessary estimates with complex absorbing potential can also be obtained via gluing from estimates for corresponding non-compact models.Comment: 16 pages, 1 figur

Nonlocality of cluster states of qubits

We investigate cluster states of qubits with respect to their non-local properties. We demonstrate that a Greenberger-Horne-Zeilinger (GHZ) argument holds for any cluster state: more precisely, it holds for any partial, thence mixed, state of a small number of connected qubits (five, in the case of one-dimensional lattices). In addition, we derive a new Bell inequality that is maximally violated by the 4-qubit cluster state and is not violated by the 4-qubit GHZ state.Comment: 5 pages; paragraph V.B contains a comparison with Guehne et al., quant-ph/041005

Energy decay for the damped wave equation under a pressure condition

We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with respect to the geodesic flow. As an application, we show an exponential decay of the energy for all initial data sufficiently regular. This decay is governed by the imaginary part of a finite number of eigenvalues close to the real axis.Comment: 32 page

Non-Invasive Measurement of Hemoglobin: Assessment of Two Different Point-of-Care Technologies

Measurement of blood hemoglobin (Hb) concentration is a routine procedure. Using a non-invasive point-of-care device reduces pain and discomfort for the patient and allows time saving in patient care. The aims of the present study were to assess the concordance of Hb levels obtained non-invasively with the Pronto-7 monitor (version 2.1.9, Masimo Corporation, Irvine, USA) or with the NBM-200MP monitor (Orsense, Nes Ziona, Israel) and the values obtained from the usual colorimetric method using blood samples and to determine the source of discordance.We conducted two consecutive prospective open trials enrolling patients presenting in the emergency department of a university hospital. The first was designed to assess Pronto-7™ and the second NBM-200MP™. In each study, the main outcome measure was the agreement between both methods. Independent factors associated with the bias were determined using multiple linear regression. Three hundred patients were prospectively enrolled in each study. For Pronto-7™, the absolute mean difference was 0.56 g.L(-1) (95% confidence interval [CI] 0.41 to 0.69) with an upper agreement limit at 2.94 g.L(-1) (95% CI [2.70;3.19]), a lower agreement limit at -1.84 g.L(-1) (95% CI [-2.08;-1.58]) and an intra-class correlation coefficient at 0.80 (95% CI [0.74;0.84]). The corresponding values for the NBM-200MP™ were 0.21 [0.02;0.39], 3.42 [3.10;3.74], -3.01 [-3.32;-2.69] and 0.69 [0.62;0.75]. Multivariate analysis showed that age and laboratory values of hemoglobin were independently associated with the bias when using Pronto-7™, while perfusion index and laboratory value of hemoglobin were independently associated with the bias when using NBM-200MP™.Despite a relatively limited bias in both cases, the large limits of agreement found in both cases render the clinical usefulness of such devices debatable. For both devices, the bias is independently and inversely associated with the true value of hemoglobin.ClinicalTrials.gov NCT01321580 and NCT01321593

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements