Related papers: Random band matrix approach to chaotic scattering:…
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…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
We derive the explicit expression for the distribution of resonance widths in a chaotic quantum system coupled to continua via M equivalent open channels. It describes a crossover from the $\chi^2$ distribution (regime of isolated…
We review the random matrix theory describing elastic scattering through zero-dimensional ballistic cavities (having chaotic classical dynamics) and quasi-one dimensional disordered systems. In zero dimension, general symmetry…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
The application of random matrix theory to scattering requires introduction of system-specific information. This paper shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically…
The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of…
A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…
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…
We consider the statistics of time delay in a chaotic cavity having $M$ open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay…
Random matrix theory can be used to describe the transport properties of a chaotic quantum dot coupled to leads. In such a description, two approaches have been taken in the literature, considering either the Hamiltonian of the dot or its…
The statistical model proposed in an accompanying paper is generalized to treat multiport scattering problems. Attention is first focused on two-port lossless systems and the model is shown to be consistent with Random Matrix Theory. The…
In this work we present a method for generating random matrices describing electromagnetic scattering from disordered media containing dielectric particles with prescribed single particle scattering characteristics. Resulting scattering…
We study complex eigenvalues of large $N\times N$ symmetric random matrices of the form ${\cal H}=\hat{H}-i\hat{\Gamma}$, where both $\hat{H}$ and $\hat{\Gamma}$ are real symmetric, $\hat{H}$ is random Gaussian and $\hat{\Gamma}$ is such…
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 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.…
Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic…
An important parameter to characterize the scattering matrix S for quantum-chaotic scattering is the width Gamma_{corr} of the S-matrix autocorrelation function. We show that the "Weisskopf estimate" d/(2pi) sum_c T_c (where d is the mean…
We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball…
We report on experimental studies of the distribution of the off-diagonal elements of the scattering matrix of open microwave networks with symplectic symmetry and a chaotic wave dynamics. These consist of two geometrically identical…