Related papers: Statistical properties of random scattering matric…
This paper concerns time-dependent scattering theory and in particular the concept of time delay for a class of one-dimensional anisotropic quantum systems. These systems are described by a Schr\"{o}dinger Hamiltonian $H = -\Delta + V$ with…
Motivated by recent experiments, the theoretical study of wave propagation in time varying materials is of current interest. Although significant in nearly all such experiments, material dispersion is commonly neglected in theoretical…
Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated…
The concepts of Wigner time delay and Wigner-Smith matrix allow to characterize temporal aspects of a quantum scattering process. The article reviews the statistical properties of the Wigner time delay for disordered systems; the case of…
Wave scattering in chaotic systems with a uniform energy loss (absorption) is considered. Within the random matrix approach we calculate exactly the energy correlation functions of different matrix elements of impedance or scattering…
We present an analytic random matrix theory for the effect of incomplete channel control on the measured statistical properties of the scattering matrix of a disordered multiple-scattering medium. When the fraction of the controlled input…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
Harmonic generation in the scattered fields produced by a dielectric sphere coated with a time-varying conductive shell is studied using a Mie theory approach hybridized with conversion matrix methods. Analytic results are derived for plane…
Elastic waves scattering off a periodic single and double array of thin cylindrical defects is considered for isotropic materials. An analytical expression for the scattering matrix is obtained by means of the Lippmann-Schwinger formalism…
We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of 3 to 16 GHz. Below 10.1 GHz the…
We consider the statistics of the scattering coefficient S of a chaotic microwave cavity coupled to a single port. We remove the non-universal effects of the coupling from the experimental S data using the radiation impedance obtained…
We study the quantum and classical scattering of Hamiltonian systems whose chaotic saddle is described by binary or ternary horseshoes. We are interested in parameters of the system for which a stable island, associated with the inner…
Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…
Random band matrices relevant for open chaotic systems are introduced and studied. The scattering model based on such matrices may serve for the description of preequilibrium chaotic scattering. In the limit of a large number of open…
We argue that one cannot correctly calculate the elastic scattering S-matrix for high-energy dipole-dipole scattering, in the region where S is small, without taking fluctuations into account. The relevant fluctuations are rare and…
We study the effects of scattering lengths on L\'evy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk…
We study the evolution of the distribution of eigenvalues of $N\times N$ matrix ensembles subject to a change of variances of its matrix elements. Our results indicate that the evolution of the probability density is governed by a Fokker-…
Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four…
In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's…
We extend the application of the concept of structural invariance to bounded time independent systems. This concept, previously introduced by two of us to argue that the connection between random matrix theory and quantum systems with a…