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It is shown that probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a characteristic shape. Such distributions could be used as a signature of chimera states, particularly in systems for which the…
The scattering properties of randomly layered optical media with ${\cal PT}$-symmetric index of refraction are studied using the transfer-matrix method. We find that the transmitance decays exponentially as a function of the system size,…
The statistical properties of a Hamiltonian $H_0$ perturbed by a localized scatterer are considered. We prove that when $H_0$ describes a bounded chaotic motion, the universal part of the spectral statistics are not changed by the…
We analyze coherent wave transport in a new physical setting associated with multimode wave systems where reflection is completely suppressed and mode-dependent losses together with mode-mixing are dictating the wave propagation. An…
A numerical study of the statistics of transmission ($t$) and reflection ($r$) of quasi-particles from a one-dimensional disordered lasing or amplifying medium is presented. The amplification is introduced via a uniform imaginary part in…
We investigate the {\em survival-return} probability distribution and the eigenspectrum for the transition probability matrix, for diffusion in the presence of perfectly absorbing traps distributed with critical disorder in two and three…
The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a…
Statistical properties of the transmittance ($T$) and reflectance ($R$) of an amplifying layer with one-dimensional disorder are investigated analytically. Whereas the transmittance at typical realizations decreases exponentially with the…
We employ the Random Matrix Theory framework to calculate the density of zeroes of an $M$-channel scattering matrix describing a chaotic cavity with a single localized absorber embedded in it. Our approach extends beyond the weak-coupling…
Complex quantum systems consisting of large numbers of strongly coupled states exhibit characteristic level repulsion, leading to a non-Poisson spacing distribution which can be described by Random Matrix Theory. Scattering resonances…
When waves impinge on a disordered material they are back-scattered and form a highly complex interference pattern. Suppressing any such distortions in the free propagation of a wave is a challenging task with many applications in a number…
We present a propagation model showing that a transmitter randomly positioned in space generates unbounded peaks in the histogram of the resulting power, provided the signal strength is an oscillating or non-monotonic function of distance.…
Energy of propagating electromagnetic waves can be fully absorbed in a thin lossy layer, but only in a narrow frequency band, as follows from the causality principle. On the other hand, it appears that there are no fundamental limitations…
It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory we derive numerical and in particular…
The universal bimodal distribution of transmission eigenvalues in lossless diffusive systems un- derpins such celebrated phenomena as universal conductance fluctuations, quantum shot noise in condensed matter physics and enhanced…
Light propagation through a normal medium is determined not only by the real part of the refractive index but also by its imaginary part, which represents optical gain and loss. Therefore, two media with different gain and loss landscapes…
Using the Random Matrix Theory approach we derive explicit distributions of the real and imaginary parts for off-diagonal entries of the Wigner reaction matrix $\mathbf{K}$ for wave chaotic scattering in systems with and without…
The reflection and transmission amplitudes of waves in disordered multimode waveguides are studied by means of numerical simulations based on the invariant embedding equations. In particular, we analyze the influence of surface-type…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
We are interested in finding the joint distribution function of the real and imaginary parts of the local Green function for a system with chaotic internal wave scattering and a uniform energy loss (absorption). For a microwave cavity…