Universality of weakly bound dimers and Efimov trimers close to Li-Cs Feshbach resonances

We study the interspecies scattering properties of ultracold Li-Cs mixtures in their two energetically lowest spin channels in the magnetic field range between 800 G and 1000 G. Close to two broad Feshbach resonances we create weakly bound LiCs dimers by radio-frequency association and measure the dependence of the binding energy on the external magnetic field strength. Based on the binding energies and complementary atom loss spectroscopy of three other Li-Cs s-wave Feshbach resonances we construct precise molecular singlet and triplet electronic ground state potentials using a coupled-channels calculation. We extract the Li-Cs interspecies scattering length as a function of the external field and obtain almost a ten-fold improvement in the precision of the values for the pole positions and widths of the s-wave Li-Cs Feshbach resonances as compared to our previous work [Pires \textit{et al.}, Phys. Rev. Lett. \textbf{112}, 250404 (2014)]. We discuss implications on the Efimov scenario and the universal geometric scaling for LiCsCs trimers

Conformal scattering for a nonlinear wave equation on a curved background

The purpose of this paper is to establish a geometric scattering result for a conformally invariant nonlinear wave equation on an asymptotically simple spacetime. The scattering operator is obtained via trace operators at null infinities. The proof is achieved in three steps. A priori linear estimates are obtained via an adaptation of the Morawetz vector field in the Schwarzschild spacetime and a method used by H\"ormander for the Goursat problem. A well-posedness result for the characteristic Cauchy problem on a light cone at infinity is then obtained. This requires a control of the nonlinearity uniform in time which comes from an estimates of the Sobolev constant and a decay assumption on the nonlinearity of the equation. Finally, the trace operators on conformal infinities are built and used to define the conformal scattering operator

Universal three-body recombination and Efimov resonances in an ultracold Li-Cs mixture

We study Efimov resonances via three-body loss in an ultracold two-component gas of fermionic $^6$Li and bosonic $^{133}$Cs atoms close to a Feshbach resonance at 843~G, extending results reported previously [Pires \textit{et al.}, Phys. Rev. Lett. 112, 250404 (2014)] to temperatures around 120~nK. The experimental scheme for reaching lower temperatures is based upon compensating the gravity-induced spatial separation of the mass-imbalanced gases with bichromatic optical dipole traps. We observe the first and second excited Li-Cs-Cs Efimov resonance in the magnetic field dependence of the three-body event rate constant, in good agreement with the universal zero-range theory at finite temperature [Petrov and Werner, Phys. Rev. A 92, 022704 (2015)]. Deviations are found for the Efimov ground state, and the inelasticity parameter $\eta$ is found to be significantly larger than those for single-species systems

Simple Three-Integral Scale-Free Galaxy Models

The Jeans equations give the second moments or stresses required to support a stellar population against the gravity field. A general solution of the Jeans equations for arbitrary axisymmetric scale-free densities in flattened scale-free potentials is given. A two-parameter subset of the solution for the second moments for the self-consistent density of the power-law models, which have exactly spheroidal equipotentials, is examined in detail. In the spherical limit, the potential of these models reduces to that of the singular power-law spheres. We build the physical three-integral distribution functions that correspond to the flattened stellar components. Next, we attack the problem of finding distribution functions associated with the Jeans solutions in flattened scale-free potentials. The third or partial integral introduced by de Zeeuw, Evans and Schwarzschild for Binney's model is generalised to thin and near-thin orbits moving in arbitrary axisymmetric scale-free potentials. The partial integral is a modification of the total angular momentum. For the self-consistent power-law models, we show how this enables the construction of simple three-integral distribution functions. The connexion between these approximate distribution functions and the Jeans solutions is discussed in some detail.Comment: 14 pages, 7 postscript figures, to appear in Monthly Notice

Recovering the mass and the charge of a Reissner-Nordstr\"om black hole by an inverse scattering experiment

In this paper, we study inverse scattering of massless Dirac fields that propagate in the exterior region of a Reissner-Nordstr\"om black hole. Using a stationary approach we determine precisely the leading terms of the high-energy asymptotic expansion of the scattering matrix that, in turn, permit us to recover uniquely the mass of the black hole and its charge up to a sign

Local energy decay of massive Dirac fields in the 5D Myers-Perry metric

We consider massive Dirac fields evolving in the exterior region of a 5-dimensional Myers-Perry black hole and study their propagation properties. Our main result states that the local energy of such fields decays in a weak sense at late times. We obtain this result in two steps: first, using the separability of the Dirac equation, we prove the absence of a pure point spectrum for the corresponding Dirac operator; second, using a new form of the equation adapted to the local rotations of the black hole, we show by a Mourre theory argument that the spectrum is absolutely continuous. This leads directly to our main result.Comment: 40 page

Metallic properties of magnesium point contacts

We present an experimental and theoretical study of the conductance and stability of Mg atomic-sized contacts. Using Mechanically Controllable Break Junctions (MCBJ), we have observed that the room temperature conductance histograms exhibit a series of peaks, which suggests the existence of a shell effect. Its periodicity, however, cannot be simply explained in terms of either an atomic or electronic shell effect. We have also found that at room temperature, contacts of the diameter of a single atom are absent. A possible interpretation could be the occurrence of a metal-to-insulator transition as the contact radius is reduced, in analogy with what it is known in the context of Mg clusters. However, our first principle calculations show that while an infinite linear chain can be insulating, Mg wires with larger atomic coordinations, as in realistic atomic contacts, are alwaysmetallic. Finally, at liquid helium temperature our measurements show that the conductance histogram is dominated by a pronounced peak at the quantum of conductance. This is in good agreement with our calculations based on a tight-binding model that indicate that the conductance of a Mg one-atom contact is dominated by a single fully open conduction channel.Comment: 14 pages, 5 figure