Related papers: Universality classes of quantum chaotic dissipativ…
Isometric fluctuation relations are deduced for the fluctuations of the order parameter in equilibrium systems of condensed-matter physics with broken discrete or continuous symmetries. These relations are similar to their analogues…
Scattering theoretical network models for general coherent wave mechanical systems with quenched disorder are investigated. We focus on universality classes for two dimensional systems with no preferred orientation: Systems of spinless…
We investigate the effect of spatial symmetries on phase coherent electronic transport through chaotic quantum dots. For systems which have a spatial symmetry that interchanges the source and drain leads, we find in the framework of random…
In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parameterized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…
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…
Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum…
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…
Absorption yields an additional exponential decay in open quantum systems which can be described by shifting the (scattering) energy E along the imaginary axis, E+i\hbar/2\tau_{a}. Using the random matrix approach, we calculate analytically…
Using the random matrix description of open quantum chaotic systems we calculate in closed form the universal autocorrelation function and the probability distribution of the total photodissociation cross section in the regime of quantum…
We consider wave propagation in a complex structure coupled to a finite number $N$ of scattering channels, such as chaotic cavities or quantum dots with external leads. Temporal aspects of the scattering process are analysed through the…
Complete eigenvalue spectra of the staggered Dirac operator in quenched $4d$ compact QED are studied on $8^3 \times 4$ and $8^3 \times 6$ lattices. We investigate the behavior of the nearest-neighbor spacing distribution $P(s)$ as a measure…
The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor and its moments in interacting chaotic few- and…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…
The fluctuations and correlations of matrix elements of cross sections are investigated in open systems that are chaotic in the classical limit. The form of the correlation functions is discussed within a statistical analysis and tested in…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…
We study the sampling complexity of a probability distribution associated with an ensemble ofidentical noninteracting bosons undergoing a quantum random walk on a one-dimensional lattice.With uniform nearest-neighbor hopping we show that…
We have performed an experiment to demonstrate the approximate time reversal of a "chaotic" time evolution of atomic deBroglie waves. We use ultra cold atoms from a Bose-Einstein condensate in a quantum $\delta$-kicked rotor experiment, and…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null…