Green operators for low regularity spacetimes

In this paper we define and construct advanced and retarded Green operators for the wave operator on spacetimes with low regularity. In order to do so we require that the spacetime satisfies the condition of generalised hyperbolicity which is equivalent to well- posedness of the classical inhomogeneous problem with zero initial data where weak solutions are properly supported. Moreover, we provide an explicit formula for the kernel of the Green operators in terms of an arbitrary eigenbasis of H 1 and a suitable Green matrix that solves a system of second order ODEs

The Black Hole: Scatterer, Absorber and Emitter of Particles

Accurate and powerful computational methods developed by the author for the wave scattering by black holes allow to obtain the highly non trivial total absorption spectrum of the Black Hole. As well as partial wave phase shifts and cross sections (elastic and inelastic), the angular distribution of absorbed and scattered waves, and the Hawking emission rates. The exact total absorption spectrum of waves by the Black Hole has as a function of frequency a remarkable oscillatory behaviour characteristic of a diffraction pattern. This is an unique distinctive feature of the black hole absorption, and due to its r = 0 singularity. Ordinary absorptive bodies and optical models do not present these features. The unitarity optical theorem is generalized to the Black Hole case explicitly showing that absorption ocurrs only at the origin. All these results allow to understand and reproduce the Black Hole absorption spectrum in terms of Fresnel-Kirchoff diffraction theory: by the interference of the absorbed rays arriving at the origin through different optical paths. These fundamental features of the Black Hole Absorption will be present for generic higher dimensional Black Hole backgrounds, and whatever the low energy effective theory they arise from. In recent and increasing litterature devoted to compute absorption cross sections (grey body factors) of black holes (whatever ordinary, stringy, D-braned), the fundamental remarkable features of the Black Hole Absorption spectrum are overlooked.Comment: 19 pages Latex, 4 ps Figures, uses epsfig and psfra

Generalised hyperbolicity in spacetimes with string-like singularities

In this paper we present well-posedness results of the wave equation in $H^{1}$ for spacetimes that contain string-like singularities. These results extend a framework able to characterise gravitational singularities as obstruction to the dynamics of test fields rather than point particles. In particular, we discuss spacetimes with cosmic strings and the relation of our results to the Strong Cosmic Censorship Conjecture.Comment: Accepted for publication in Classical and Quantum Gravit

A salary system for the assignment problem

We propose a modification to the concept of the potential of agame à la Hart-Mas Colell to determine a salary system for theassignment problem. We obtain explicit formulas for the potentialof the assignment problem and for it's corresponding salarysystem. Also, we establish some properties of this salary systemand we give an interpretation in terms of the Shapley value.assignment problem

Additive Combination Spaces

We introduce a class of metric spaces called $p$-additive combinations and show that for such spaces we may deduce information about their $p$-negative type behaviour by focusing on a relatively small collection of almost disjoint metric subspaces, which we call the components. In particular we deduce a formula for the $p$-negative type gap of the space in terms of the $p$-negative type gaps of the components, independent of how the components are arranged in the ambient space. This generalizes earlier work on metric trees by Doust and Weston. The results hold for semi-metric spaces as well, as the triangle inequality is not used.Comment: 17 page

Nonlinear chiral refrigerators

We investigate a mesoscopic refrigerator based on chiral quantum Hall edge channels. We discuss a three-terminal cooling device in which charge transport occurs between a pair of voltage-biased terminals only. The third terminal, which is to be cooled, is set as a voltage probe with vanishing particle flux. This largely prevents the generation of direct Joule heating which ensures a high coefficient of performance. Cooling operation is based on energy-dependent quantum transmissions. The latter are implemented with the aid of two tunable scattering resonances (quantum dots). To find the optimal performance point and the largest temperature difference created with our refrigerator, it is crucial to address the nonlinear regime of transport, accounting for electron-electron interaction effects. Our numerical simulations show that the maximal cooling power can be tuned with the quantum dot couplings and energy levels. Further, we provide analytical expressions within a weakly nonlinear scattering-matrix formalism which allow us to discuss the conditions for optimal cooling in terms of generalized thermopowers. Our results are important for the assessment of chiral conductors as promising candidates for efficient quantum refrigerators with low dissipation.Comment: 9 pages, 4 figures. v2: minor changes. Published versio