Related papers: Universal Frequency Correlations and Recurrence St…
We present a discrete model of resonant scattering of waves by an open periodic waveguide. The model elucidates a phenomenon common in electromagnetics, in which the interaction of plane waves with embedded guided modes of the waveguide…
We use the Random Matrix Theory (RMT) to study the probability distribution function and moments of the wave power transmitted inside systems with ergodic wave motion. The results describe either open multichannel systems or their closed…
The puzzle of "sticky collisions," in which molecular collision complexes exhibit unexpectedly long lifetimes, remains an unresolved mystery. A central challenge to solving this mystery is that traditional close-coupling calculations remain…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
The emergence of nonequilibrium phenomena in individual complex wave systems has long been of fundamental interests. Its analytic studies remain notoriously difficult. Using the mathematical tool of the concentration of measure (CM), we…
We investigate the linear correlation coefficient between the intensities at different wavelengths in photospheric and chromospheric spectral lines. Waves that propagate vertically through the stratified solar atmosphere affect different…
A novel methodology to unleash electromagnetic coupling matrix information in coupled-resonator microwave circuits has been recently proposed [1]. This information is derived from Maxwell's equations and the natural language of…
We review known and discuss new signatures of high-intensity Compton scattering assuming a scenario where a high-power laser is brought into collision with an electron beam. At high intensities one expects to see a substantial red-shift of…
The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…
We compute spectra of large stochastic matrices $W$, defined on sparse random graphs, where edges $(i,j)$ of the graph are given positive random weights $W_{ij}>0$ in such a fashion that column sums are normalized to one. We compute spectra…
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…
Radio pulsars exhibit several unexplained phenomena, in particular the average pulse profiles with the apparent core-cone structure and interesting frequency evolution. I show that they can be interpreted through essential geometric…
We analyze general enough models of repeated indirect measurements in which a quantum system interacts repeatedly with randomly chosen probes on which Von Neumann direct measurements are performed. We prove, under suitable hypotheses, that…
Waves propagating through a weakly scattering random medium show a pronounced branching of the flow accompanied by the formation of freak waves, i.e., extremely intense waves. Theory predicts that this strong fluctuation regime is…
The use of correlation matrices to evaluate the number of uncorrelated stirrer positions of reverberation chamber has widespread applications in electromagnetic compatibility. We present a comparative study of recent techniques based on…
We present experimental results on a model system for studying wave propagation in a complex medium exhibiting low frequency resonances. These experiments enable us to investigate a fundamental question that is relevant for many materials,…
We present an analysis of wave propagation in a two step-index, parallel waveguide system. The goal is to quantify the effect of scattering at randomly perturbed interfaces between the guiding layers of high index of refraction and the host…
We establish a general framework to explore parametric statistics of individual energy levels in unitary random matrix ensembles. For a generic confinement potential $W(H)$, we (i) find the joint distribution functions of the eigenvalues of…
Recent experiments on quantum dots in the Coulomb Blockade regime have shown how adding successive electrons into a dot modifies the energy spectrum and the wave functions of the electrons already present in the dot. Using a microscopic…
We have employed the method of spectral moments to study the density of vibrational states and the Raman coupling coefficient of large 2- and 3- dimensional percolators at threshold and at higher concentration. We first discuss the over-and…