Related papers: Generalized random matrix conjecture for chaotic s…
Quantum counterparts of certain simple classical systems can exhibit chaotic behaviour through the statistics of their energy levels and the irregular spectra of chaotic systems are modelled by eigenvalues of infinite random matrices. We…
We present a non-perturbative analysis of the power-spectrum of energy level fluctuations in fully chaotic quantum structures. Focussing on systems with broken time-reversal symmetry, we employ a finite-$N$ random matrix theory to derive an…
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…
It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the behavior of the power spectrum of the excitation energy fluctuations, which is…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
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…
Quantum chaotic systems exhibit certain universal statistical properties that closely resemble predictions from random matrix theory (RMT). With respect to observables, it has recently been conjectured that, when truncated to a sufficiently…
We study the universal structure of late-time ensembles obtained from unitary dynamics in quantum chaotic systems with symmetries, such as charge or energy conservation. We find that although quantum states do not ergodically explore the…
Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum…
The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…
In the framework of a random matrix description of chaotic quantum scattering the positions of $S-$matrix poles are given by complex eigenvalues $Z_i$ of an effective non-Hermitian random-matrix Hamiltonian. We put forward a conjecture on…
For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of the observable. In this paper we study…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
It is commonly expected that for quantum chaotic many body systems, the statistical properties approach those of random matrices when increasing the system size. We demonstrate for various kicked spin-1/2 chain models that the average…
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…
Consider $D$ random systems that are modeled by independent $N\times N$ complex Hermitian Wigner matrices. Suppose they are lying on a circle and the neighboring systems interact with each other through a deterministic matrix $A$. We prove…
In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's…
A conjecture due to Bohigas, Giannoni and Schmit (BGS), stating that the energy level correlations of quantum chaotic systems generically obey the laws of random matrix theory, is given a precise formulation for quantized symplectic maps.…