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Chaotic scattering in complex systems

- Leader : Legrand Olivier

- Collaborators within the LPMC : Kuhl Ulrich, Mortessagne Fabrice

- External Collaborators : Savin D. (Department of Mathematical Sciences, Brunel University, UK), Richalot E. and Picon O. (ESYCOM, Université Paris-Est Marne la Vallée)

- PhD students/Post-doctoral fellows : Gros Jean-Baptiste, Selemani Kamardine

- Financial supports : ANR CAOREV (ANR-2011-BS0300302 (2012/2014)) [1]

- Description :

Since the beginning of the century, the Wave Chaos community has been interested in describing the spectral and spatial statistical properties of more realistic systems considered as open, involving coupling mechanisms with the outside, such as losses by absorption or leakage through radiation. More particularly, by applying the theory of the Random Non-Hermitian Matrices to the formalism of the effective Hamiltonian, which takes into account the effect of losses, analytical results, concerning the spectral and spatial statistics of open chaotic systems, have been established at LPMC. In particular, they could relate the parameter of non-orthogonality of the modes to their spectral width, and analytically derive the statistical distributions of both quantities. One of our collaborators (D. Savin) has recently proposed to study the effect of the non-orthogonality of modes on the statistics of parametrically induced width shifts. In our group, at LPMC, an experimental verification of his predictions have just been achieved in a two-dimensional (2D) microwave cavity, where parametric modifications were obtained by moving a wall of the cavity or one of several metallic scatterers placed inside. Thanks to this kind of experimental system, we may investigate the transition of complex quasi-modes as the absorption is varied. Inside 2D microwave cavities, we can also study the effect of losses on the distribution of spacings between adjacent resonant frequencies by testing recent predictions involving a number of coupling channels.

The important increase of wireless communication and the use of an ever growing range of frequencies has a strong impact on the pollution of the electromagnetic environment. The interaction between electromagnetic (em) waves and electronic devices require a precise quantification of the em perturbation to ensure the good working order of communicating devices. This is the aim of Electro-Magnetic Compatibility (EMC). The Mode-stirred Reverberation Chamber (MSRC) is one of the fundamental tools to perform such EMC measurements. Using the knowledge of the LPMC on waves in open chaotic systems and on the interaction of microwaves with metallic chaotic cavities, our present research is dedicated to a proper modeling of optimized shapes of actual RCs including fundamental investigations about the role of Ohmic losses and of inclusions such as mobile stirrers. Recent results concerning the regime of moderate modal overlap have been obtained through numerical simulations of actual MSRCs and are to be validated in actual experiments led in one the MSRC of ESYCOM made chaotic by adding metallic hemispheres on walls.

The EMC community, to which our partners of ESYCOM belong, has started showing a growing interest in our works, which are likely to contribute to change the norms currently used in the domain of MSRCs applied to EMC.

[1] Titre : Apport de la théorie du chaos ondulatoire pour l’étude et l’optimisation des chambres réverbérantes.

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MOSAIQ, Physique Mésoscopique