Related papers: Intensity statistics inside an open wave-chaotic c…
We propose an information-theoretic model for the transport of waves through a chaotic cavity in the presence of absorption. The entropy of the S-matrix statistical distribution is maximized, with the constraint $<Tr SS^{\dagger}> =\alpha…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
Waves propagate through disordered systems in a variety of regimes. There is a threshold of disorder beyond which waves become localized and transport becomes restricted. The intensity I of the wave transmitted through a system has a…
We discuss a model for studying the statistical properties of the impedance ($Z$) and scattering ($S$) matrices of open electromagnetic cavities with several transmission lines or waveguides connected to the cavity. In this paper, we mainly…
We study the intensity distribution function, P(I), for monochromatic waves propagating in quasi one-dimensional disordered medium, assuming that a point source and a point detector are embedded in the bulk of the medium. We find deviations…
The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally tree-like, and sparse covariance matrices. We derive a…
An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although…
Structures with heavy-tailed distributions of disorder occur widely in nature. The evolution of such systems, as in foraging for food or the occurrence of earthquakes is generally analyzed in terms of an incoherent series of events. But the…
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…
We consider the intensity pattern, generated by a monochromatic source, in a disordered cavity coupled to the environment. For weak coupling, and when the source frequency is tuned to a resonance, the intensity distribution is close to…
In this letter, we demonstrate that a non-Hermitian Random Matrix description can account for both spectral and spatial statistics of resonance states in a weakly open chaotic wave system with continuously distributed losses. More…
We establish large deviation formulas for linear statistics on the $N$ transmission eigenvalues $\{T_i\}$ of a chaotic cavity, in the framework of Random Matrix Theory. Given any linear statistics of interest $A=\sum_{i=1}^N a(T_i)$, the…
A theoretical analysis of the statistical distributions of the reflected intensities from random media is presented. We use random matrix theory to analytically deduce the probability densities in the localization regime. Numerical…
Asymptotic behavior of a class of nonlinear Schr\"odinger equations are studied. Particular cases of 1D weakly focusing and Bose-Einstein condensates are considered. A statistical approach is presented to describe the stationary probability…
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…
We conjecture that in chaotic quantum systems with escape the intensity statistics for resonance states universally follows an exponential distribution. This requires a scaling by the multifractal mean intensity which depends on the system…
We consider the statistics of the impedance of a chaotic microwave cavity coupled to a single port. We remove the non-universal effects of the coupling from the experimental data using the radiation impedance obtained directly from the…
The spectral densities of ensembles of non-Hermitian sparse random matrices are analysed using the cavity method. We present a set of equations from which the spectral density of a given ensemble can be efficiently and exactly calculated.…
We consider a guided Bose-Einstein matter wave flowing through a disordered potential. We determine the critical velocity at which superfluidity is broken and compute its statistical properties. They are shown to be connected to extreme…
In this letter, we investigate the statistical properties of electromagnetic signals after different times of duration within one-dimensional local-disordered time-varying cavities, where both spatial and temporal disorders are added. Our…