Related papers: Statistical properties of resonance widths for ope…
We consider two random matrix ensembles which are relevant for describing critical spectral statistics in systems with multifractal eigenfunction statistics. One of them is the Gaussian non-invariant ensemble which eigenfunction statistics…
We establish several properties of the integrated density of states for random quantum graphs: Under appropriate ergodicity and amenability assumptions, the integrated density of states can be defined using an exhaustion procedure by…
The conception of new metamaterials showing unorthodox behaviors with respect to elastic wavepropagation has become possible in recent years thanks to powerful dynamical homogenization techniques. Such methods effectively allow to describe…
Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of…
Motivated by recent studies of the phenomenon of Coherent Perfect Absorption, we develop the random matrix theory framework for understanding statistics of the zeros of the (subunitary) scattering matrices in the complex energy plane, as…
Sound propagation in a waveguide lined with one section of locally reactive material is studied by resonance scattering approach. The objective is to understand the effects of mode coupling in the lined section on the transmission. It is…
We study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$. If the graph is "straight", i.e. periodic…
We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation…
We study families of open chaotic maps that classically share the same asymptotic properties -- forward and backwards trapped sets, repeller dimensions, escape rate -- but differ in their short time behavior. When these maps are quantized…
We investigate the coherent population trapping resonance induced by a polychromatic optical field with an asymmetric spectrum, i.e., whose sidebands equidistant from the carrier have unequal powers. A situation is considered where a…
An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an…
The points where diffraction orders emerge or vanish in the propagating spectrum of periodic non-Hermitian systems are referred to as scattering thresholds. Close to these branch points, resonances from different Riemann sheets can…
The multiple scattering model of a quantum particle in a random Lorentz gas consisting of fixed point scatterers is considered in arbitrary dimension. An efficient method is developed to numerically compute the map of the density of…
We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…
Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which…
We calculate the S-matrix correlation function for chaotic scattering on quantum graphs and show that it agrees with that of random--matrix theory (RMT). We also calculate all higher S-matrix correlation functions in the Ericson regime.…
The outcoupling of a Bose-Einstein condensate through an optical lattice provides an interesting scenario to study quantum transport phenomena or the analog Hawking effect as the system can reach a quasi-stationary black-hole configuration.…
We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric…
We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical…
We consider interaction of a femtosecond light pulse with a one-dimensional photonic crystal with relaxing cubic nonlinearity in the regime of self-trapping. By use of numerical simulations, it is shown that, under certain conditions, the…