All pages tagged Random Matrix Theory

Reverberation chambers are currently involved in a large variety of applications ranging from computational imaging to electromagnetic (EM) compatibility testing as well as the characterization of antenna efficiency, wireless devices or MIMO systems . In most of the above mentioned applications, the related measurements are based on statistical averages and their fluctuations. We introduce a very efficient mode stirring process based on electronically reconfigurable metasurfaces (ERMs) developed by the young start-up GREENERWAVE . By locally changing the field boundary conditions, the ERMs allow to generate a humongous number of uncorrelated field realizations even within small reverberation chambers. We fully experimentally characterize this stirring process by determining the number of uncorrelated realizations via the autocorrelation function of the transmissions. Thanks to the huge size of uncorrelated samples thus produced, we are able to experimentally investigate the extreme value statistics of the EM field very precisely and compare them with theorical predictions deduced from the random matrix theory (RMT). Based on the fluctuations of field's maxima, the IEC-standard uniformity criterion parameter $\sigma_\textrm{dB}$ is for instance investigated and reveals the performance of the stirring with ERM's. We compare the experimental results on the uniformity criterion parameter with a corresponding RMT model where the only parameter, the modal overlap, is extracted via the quality factor. We find a very good agreement.

The universal features of the spectra of chaotic systems are well reproduced by the corresponding quantities of the random matrix ensembles [1]. Depending on symmetry with respect to time reversal and the presence or absence of a spin 1/2 there are three ensembles: the Gaussian orthogonal (GOE), the Gaussian unitary (GUE), and the Gaussian symplectic ensemble (GSE). With a further particle-antiparticle symmetry there are in addition the chiral variants of these ensembles [2]. Relativistic quantum mechanics is not needed to realize the latter symmetry. A tight-binding system made up of two subsystems with only interactions between the subsystems but no internal interactions, such as a graphene lattice with only nearest neighbor interactions, will do it as well. First results of a microwave realization of the chiral GOE (the BDI in Cartan's notation) will be presented, where the tight-binding system has been constructed by a lattice made up of dielectric cylinders [3].

[1] O. Bohigas, M. J. Giannoni, and C. Schmit. Characterization of chaotic spectra and universality of level fluctuation laws. PRL 52, 1 (1984).

[2] C. W. J. Beenakker. Random-matrix theory of Majorana fermions and topological superconductors. Rev. Mod. Phys. 87, 1037 (2015).

[3] S. Barkhofen, M. Bellec, U. Kuhl, and F. Mortessagne. Disordered graphene and boron nitride in a microwave tight-binding analog. PRB 87, 035101 (2013).