Related papers: Spectral Statistics in the Quantized Cardioid Bill…
We report on the experimental investigation of the properties of the eigenvalues and wavefunctions and the fluctuation properties of the scattering matrix of closed and open billiards, respectively, of which the classical dynamics undergoes…
A billiard in the form of a stadium with periodically perturbed boundary is considered. Two types of such billiards are studied: stadium with strong chaotic properties and a near-rectangle billiard. Phase portraits of such billiards are…
We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random--matrix theory. The stability of these correlations with regard to non--universal corrections is analyzed in…
In a series of pump and probe experiments, we study the lifetime statistics of a quantum chaotic resonator when the number of open channels is greater than one. Our design embeds a stadium billiard into a two dimensional photonic crystal…
We use scanning near-field optical microscopy to image hyperbolic phonon polaritons in hexagonal boron nitride (hBN) billiards with integrable and chaotic geometries. In Sinai billiards, we observe irregular mode patterns consistent with…
We consider the motion of a particle subjected to the constant gravitational field and scattered inelasticaly by hard boundaries which possess the shape of parabola, wedge, and hyperbola. The billiard itself performs oscillations. The…
We study spectral statistics of lattice modes in a disordered crystal and in a crystal with a complex unit cell. The correlations of the eigenmode frequencies of a block of a disordered solid is found to obey the GOE Wigner-Dyson…
Dynamical properties of the elliptical stadium billiard, which is a generalization of the stadium billiard and a special case of the recently introduced mushroom billiards, are investigated analytically and numerically. In dependence on two…
We investigate chaotic scattering on an attractive step potential with a quadrupolar deformation. The phase space features of the bound billiard are studied by using the notion of symmetry lines to find periodic orbits. We show that the…
The statistics of energy levels of a rectangular billiard, that is perturbed by a strong localized potential, are studied analytically and numerically, when this perturbation is at the center or at a typical position. Different results are…
Billiards tables - a minimal model for particles moving in a confined region - are known to present classical (and quantum) different features according to their shape, ranging from strongly chaotic to integrable dynamics. Here we consider…
We consider a billiard model of a self-bound, interacting three-body system in two spatial dimensions. Numerical studies show that the classical dynamics is chaotic. The corresponding quantum system displays spectral fluctuations that…
We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric non--linear $\sigma$--model…
We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
We consider Hamiltonian systems which can be described both classically and quantum mechanically. Trace formulas establish links between the energy spectra of the quantum description and the spectrum of actions of periodic orbits in the…
We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles,…
We study the fluctuations that are predicted in the autocorrelation function of an energy eigenstate of a chaotic, two-dimensional billiard by the conjecture (due to Berry) that the eigenfunction is a gaussian random variable. We find an…
We characterize quantum dynamics in triangular billiards in terms of five properties: (1) the level spacing ratio (LSR), (2) spectral complexity (SC), (3) Lanczos coefficient variance, (4) energy eigenstate localisation in the Krylov basis,…
In a series of two papers we investigate the universal spectral statistics of chaotic quantum systems in the ten known symmetry classes of quantum mechanics. In this first paper we focus on the construction of appropriate ensembles of star…