In this article, we present a numerical investigation of three-dimensional electromagnetic Sinai-like cavities. We computed around 600 eigenmodes for two different geometries: a parallelepipedic cavity with one halfsphere on one wall and a parallelepipedic cavity with one half-sphere and two spherical caps on three adjacent walls. We show that the statistical requirements of a well operating reverberation chamber are better satisfied in the more complex geometry without a mechanical mode-stirrer/tuner. This is to the fact that our proposed cavities exhibit spatial and spectral statistical behaviours very close to those predicted by random matrix theory. More specifically, we show that in the range of frequency corresponding to the first few hundred modes, the suppression of non-generic modes (regarding their spatial statistics) can be achieved by reducing drastically the amount of parallel walls. Finally, we compare the influence of losses on the statistical complex response of the field inside a parallelepipedic and a chaotic cavity. We demonstrate that, in a chaotic cavity without any stirring process, the low frequency limit of a well operating reverberation chamber can be significantly reduced under the usual values obtained in mode-stirred reverberation chambers.

The change of resonance widths in an open system under a perturbation of its interior has been recently introduced by Fyodorov and Savin [Phys. Rev. Lett. 108, 184101 (2012)] as a sensitive indicator of the nonorthogonality of resonance states. We experimentally study universal statistics of this quantity in weakly open two-dimensional microwave cavities and reverberation chambers realizing scalar and electromagnetic vector fields, respectively. We consider global as well as local perturbations, and also extend the theory to treat the latter case. The influence of the perturbation type on the width shift distribution is more pronounced for many-channel systems. We compare the theory to experimental results for one and two attached antennas and to numerical simulations with higher channel numbers, observing a good agreement in all cases. The most general feature of open quantum or wave systems is the set of complex resonances. They manifest themselves in scattering through sharp energy variations of the observables and correspond to the complex poles of the S matrix. Theoretically, the latter are given by the eigenvalues E n = E n − i 2 Γ n of the effective non-Hermitian Hamiltonian H eff of the open system [1-4]. The antiHermitian part of H eff originates from coupling between the internal (bound) and continuum states, giving rise to finite resonance widths Γ n > 0. The other key feature is that the eigenfunctions of H eff are nonorthogonal [2,4]. Their nonorthogonality is crucial in many applications; it influences nuclear cross sections [5], features in decay laws of quantum chaotic systems [6], and yields excess quantum noise in open laser resonators [7]. For systems invariant under time reversal, like open microwave cavities studied below, the nonorthogonality is due to the complex wave functions, yielding the so-called phase rigidity [8][9][10] and mode complexness [11,12] Recently, such nonorthogonality was identified as the root cause for enhanced sensitivity to perturbations in open systems [17], see also Ref. [18]. Consider the parametric motion of complex resonances under internal perturbations. This can be modeled by a Hermitian term V added to H eff , so H eff = H eff + V . The complex energy shift δE n = E n − E n of the nth resonance is then given by perturbation theory for non-Hermitian operators [17,19], yielding in the leading order δE n = L n |V |R n , where L n | and |R n are the left and right eigenfunctions of H eff corresponding to E n . They form a biorthogonal system; in particular, L n |R m = δ nm but U nm ≡ L n |L m = δ nm in general. U is known in nuclear physics as the Bell-Steinberger nonorthogonality matrix [2,5], see also [20]. Crucially, a nonzero width shift δΓ n = −2Im δE n is induced solely by the off-diagonal elements of U [17]where V nm = R n |V |R m = V * mn . It vanishes only if the resonance states were orthogonal (all U m =n = 0).Note that the nonorthogonality measures studied in Refs. [7][8][9][10][11][12] are related to the diagonal elements U nn . Those and the width s...

No abstract

No abstract