Asymptotics of spherical superfunctions on rank one Riemannian symmetric superspaces

We compute the Harish-Chandra $c$-function for a generic class of rank-one purely non-compact Riemannian symmetric superspaces $X=G/K$ in terms of Euler $\Gamma$ functions, proving that it is meromorphic. Compared to the even case, the poles of the $c$-function are shifted into the right half-space. We derive the full asymptotic Harish-Chandra series expansion of the spherical superfunctions on $X$. In the case where the multiplicity of the simple root is an even negative number, they have a closed expression as Jacobi polynomials for an unusual choice of parameters.Comment: 41 pages; slightly expanded version; accepted for publication in Doc. Math (2014

Non-Euclidean Fourier inversion on super-hyperbolic space

For the super-hyperbolic space in any dimension, we introduce the non-Euclidean Helgason--Fourier transform. We prove an inversion formula exhibiting residue contributions at the poles of the Harish-Chandra c-function, signalling discrete parts in the spectrum. The proof is based on a detailed study of the spherical superfunctions, using recursion relations and localization techniques to normalize them precisely, careful estimates of their derivatives, and a rigorous analysis of the boundary terms appearing in the polar coordinate expression of the invariant integralComment: 30 pages; final version accepted for publication in Comm. Math. Phy

Photoacoustic-based gas sensing: A review

The use of the photoacoustic effect to gauge the concentration of gases is an attractive alternative in the realm of optical detection methods. Even though the effect has been applied for gas sensing for almost a century, its potential for ultra-sensitive and miniaturized devices is still not fully explored. This review article revisits two fundamentally different setups commonly used to build photoacoustic-based gas sensors and presents some distinguished results in terms of sensitivity, ultra-low detection limits, and miniaturization. The review contrasts the two setups in terms of the respective possibilities to tune the selectivity, sensitivity, and potential for miniaturization.S.P. acknowledges funding from the Community of Madrid under grant number 2016-T1/AMB-1695

Relational Contract Theory and Sovereign Debt

Relational contract theory will first be presented using principles gleaned from writings in the field 7 to craft a functional/relational model with which to approach legal practice.8 This version of relational contract will then be applied to the problem of developing country debt through description of a hypothetical sovereign loan relationship.9 By exploring the conflicts and trends of this association under a general taxonomy of relational contract, normative analysis of the restructuring process can be accomplished, contractual trends identified, and suggestions for change offered.\u2

Cold heteronuclear atom-ion collisions

We study cold heteronuclear atom ion collisions by immersing a trapped single ion into an ultracold atomic cloud. Using ultracold atoms as reaction targets, our measurement is sensitive to elastic collisions with extremely small energy transfer. The observed energy-dependent elastic atom-ion scattering rate deviates significantly from the prediction of Langevin but is in full agreement with the quantum mechanical cross section. Additionally, we characterize inelastic collisions leading to chemical reactions at the single particle level and measure the energy-dependent reaction rate constants. The reaction products are identified by in-trap mass spectrometry, revealing the branching ratio between radiative and non-radiative charge exchange processes

Entanglement dynamics under decoherence: from qubits to qudits

We investigate the time evolution of entanglement for bipartite systems of arbitrary dimensions under the influence of decoherence. For qubits, we determine the precise entanglement decay rates under different system-environment couplings, including finite temperature effects. For qudits, we show how to obtain upper bounds for the decay rates and also present exact solutions for various classes of states.Comment: 8 pages, 2 figure

Relational Contract Theory and Sovereign Debt

Relational contract theory will first be presented using principles gleaned from writings in the field 7 to craft a functional/relational model with which to approach legal practice.8 This version of relational contract will then be applied to the problem of developing country debt through description of a hypothetical sovereign loan relationship.9 By exploring the conflicts and trends of this association under a general taxonomy of relational contract, normative analysis of the restructuring process can be accomplished, contractual trends identified, and suggestions for change offered.\u2