Cône de lumière | EPFL Graph Search

redresse=1.25|vignette|Le cône de lumière centré sur un événement. En physique, le cône de lumière est une notion fondamentale de la théorie de la relativité, permettant à partir d'un événement e_0 la distinction entre les événements passés, les événements futurs et les événements inaccessibles (dans le passé comme dans le futur). Le cône de lumière est ainsi désigné à la suite de Hermann Minkowski (-). Mathématiquement, un cône de lumière est un . Dans le cadre de la relativité restreinte, les événements de l'espace-temps autres que e_0 se divisent en trois catégories : le passé absolu et le futur absolu de e_0 d'une part , et lailleurs d'autre part Les événements intérieurs au cône peuvent être liés causalement avec e_0 ; par contre les événements situés dans l'ailleurs de e_0 sont dits causalement déconnectés de e_0 et ne peuvent l'influencer ou être influencés par lui. Dans le cadre de

A stability theory beyond the co-rotational setting for critical wave maps blow up

Joachim Krieger, Shuang Miao

We exhibit non-equivariant perturbations of the blowup solutions constructed in [18] for energy critical wave maps into

\mathbb{S}^2

. Our admissible class of perturbations is an open set in some sufficiently smooth topology and vanishes near the light cone. We show that the blowup solutions from [18] are rigid under such perturbations, including the space-time location of blowup. As blowup is approached, the dynamics agrees with the classification obtained in [7], and all six symmetry parameters converge to limiting values. Compared to the previous work [16] in which the rigidity of the blowup solutions from [18] under equivariant perturbations was proved, the class of perturbations considered in the present work does not impose any symmetry restrictions. Separation of variables and decomposing into angular Fourier modes leads to an infinite system of coupled nonlinear equations, which we solve for small admissible data. The nonlinear analysis is based on the distorted Fourier transform, associated with an infinite family of Bessel type Schrödinger operators on the half-line indexed by the angular momentum

n

. A semi-classical WKB-type spectral analysis relative the parameter

\hbar=\frac{1}{n+1}

for large

|n|

allows us to effectively determine the distorted Fourier basis for the entire infinite family. Our linear analysis is based on the global Liouville-Green transform as in the earlier work [4, 5].

2020

Momentum-space conformal blocks on the light cone

Marc Gillioz

We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks. The blocks are polynomials in the cosine of the scattering angle, with degree corresponding to the spin of the intermediate operator. The coefficients of these polynomials are obtained in a closed-form expression for arbitrary spacetime dimension d > 2. If the scaling dimension of the intermediate operator is large, the conformal block reduces to a Gegenbauer polynomial f on the contrary the scaling dimension saturates the unitarity bound, the block is different Gegenbauer polynomial These results are then used as an inversion formula to compute OPE coefficients in a free theory example.

SPRINGER2018

Characterisation of photonic crystal and nanophotonics devices with Fourier optics

Romuald Houdré, Jana Jágerská, Nicolas Le Thomas

We report on the experimental investigation of the Floquet-Bloch modes propagation inside photonic crystal (PhC) structures as well as their emission from the structures with far-field optics. We demonstrate that far-field optical experiments can be used to retrieve fundamental optical properties of PhC structures, Such as the light path, the dispersion Curves above and below the light cone, and the equi-frequency Surfaces both in one and two dimensions, in a single step and without numerical post-processing.

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