Related papers: Quantum chaos and regularity in $\Phi^4$ theory
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory. As a measure of the fluctuation properties of the eigenvalues, we consider the nearest-neighbor…
The random matrix ensembles (RME) of Hamiltonian matrices, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applicable to following quantum statistical systems: nuclear systems, molecular…
We compute numerically eigenvalues and eigenfunctions of the quantum Hamiltonian that describes the quantum mechanics of a point particle moving freely in a particular three-dimensional hyperbolic space of finite volume and investigate the…
We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective…
Recent theoretical studies of chaotic scattering have encounted ensembles of random matrices in which the eigenvalue probability density function contains a one-body factor with an exponent proportional to the number of eigenvalues. Two…
Using Random Matrix Theory one can derive exact relations between the eigenvalue spectrum of the covariance matrix and the eigenvalue spectrum of its estimator (experimentally measured correlation matrix). These relations will be used to…
Understanding the emergence of chaos in many-body quantum systems away from semi-classical limits, particularly in spatially local interacting spin Hamiltonians, has been a long-standing problem. In these intrinsically quantum regimes,…
We introduce randomness into a class of integrable models and study the spectral form factor as a diagnostic to distinguish between randomness and chaos. Spectral form factors exhibit a characteristic dip-ramp-plateau behavior in the $N>2$…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
A multifractal analysis is performed on the universality classes of random matrices and the transition ones.Our results indicate that the eigenvector probability distribution is a linear sum of two chi-squared distribution throughout the…
We study heavy-tailed Hermitian random matrices that are unitarily invariant. The invariance implies that the eigenvalue and eigenvector statistics are decoupled. The motivating question has been whether a freely stable random matrix has…
We argue semiclassically, on the basis of Gutzwiller's periodic-orbit theory, that full classical chaos is paralleled by quantum energy spectra with universal spectral statistics, in agreement with random-matrix theory. For dynamics from…
For many classically chaotic systems, it is believed that in the semiclassical limit, the matrix elements of smooth observables approach the phase space average of the observable. In the approach to the limit the matrix elements can…
In the framework of perturbation theory the reality of the perturbed eigenvalues of a class of $\PT$symmetric Hamiltonians is proved using stability techniques. We apply this method to $\PT$symmetric unperturbed Hamiltonians perturbed by…
We provide compelling evidence for the presence of quantum chaos in the unitary part of Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the…
We study the characteristic polynomial of Haar distributed random unitary matrices. We show that after a suitable normalization, as one increases the size of the matrix, powers of the absolute value of the characteristic polynomial as well…
The concept of concurrence is researched to characterize the dynamical behavior of the bipartite systems. The quantum kicked top model has great significance in the qubit systems and the chaotic properties of the entanglement. The…
We investigate the eigenvalues statistics of ensembles of normal random matrices when their order N tends to infinite. In the model the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We…