Related papers: Spectral statistics in an open parametric billiard…
Predicting the statistics of realistic wave-chaotic scattering systems requires, in addition to random matrix theory, introduction of system-specific information. This paper investigates experimentally one aspect of system-specific…
The seminal physical model for investigating formulations of nonlinear dynamics is the billiard. Gravitational billiards provide an experimentally accessible arena for their investigation. We present a mathematical model that captures the…
The level dynamics of pseudointegrable systems with different genus numbers $g$ is studied experimentally using microwave cavities. For higher energies the distribution of the eigenvalue velocities is Gaussian, as it is expected for chaotic…
We develop a statistical description of chaotic wavefunctions in closed systems obeying arbitrary boundary conditions by combining a semiclassical expression for the spatial two-point correlation function with a treatment of eigenfunctions…
With a perturbation body technique intensity distributions of the electric field strength in a flat microwave billiard with a barrier inside up to mode numbers as large as about 700 were measured. A method for the reconstruction of the…
We study the quantal energy spectrum of triangular billiards on a spherical surface. Group theory yields analytical results for tiling billiards while the generic case is treated numerically. We find that the statistical properties of the…
Bayesian inference is applied to the level fluctuations of two coupled microwave billiards in order to extract the coupling strength. The coupled resonators provide a model of a chaotic quantum system containing two coupled symmetry classes…
We study the statistics of the experimental eigenfunctions of chaotic and disordered microwave billiards in terms of the moments of their spatial distributions, such as the Inverse Participation Ratio (IPR) and density-density…
Using semi-classical formalism and asymptotic proliferation law of periodic orbits, we obtain an analytical expressions for the two-level cluster function, spectral form factor, level spacing distribution and the number variance for…
In this paper, we show that two-dimensional billiards with point interactions inside exhibit a chaotic nature in the microscopic world, although their classical counterpart is non-chaotic. After deriving the transition matrix of the system…
We present scanning-probe images and magnetic-field plots which reveal fractal conductance fluctuations in a quantum billiard. The quantum billiard is drawn and tuned using erasable electrostatic lithography, where the scanning probe draws…
We clarify from a general perspective, the condition for the appearance of chaotic energy spectrum in quantum pseudointegrable billiards with a point scatterer inside.
The conductance through open quantum dots or quantum billiards shows fluctuations, that can be explained as interference between waves following different paths between the leads of the billiard. We examine such systems by the use of a…
This article presents a new method to calculate eigenvalues of right triangle billiards. Its efficiency is comparable to the boundary integral method and more recently developed variants. Its simplicity and explicitness however allow new…
In this article we study the fluctuation of linear statistics of eigenvalues of circulant, symmetric circulant, reverse circulant and Hankel matrices. We show that the linear spectral statistics of these matrices converges to the Gaussian…
Generic one-parameter billiards are studied both classically and quantally. The classical dynamics for the billiards makes a transition from regular to fully chaotic motion through intermediary soft chaotic system. The energy spectra of the…
The dynamics of chaotic billiards is significantly influenced by coexisting regions of regular motion. Here we investigate the prevalence of a different fundamental structure, which is formed by marginally unstable periodic orbits and…
The study of electron motion in semiconductor billiards has elucidated our understanding of quantum interference and quantum chaos. The central assumption is that ionized donors generate only minor perturbations to the electron…
Using the one-to-one correspondence between the Poynting vector in a microwave billiard and the probability current density in the corresponding quantum system probability densities and currents were studied in a microwave billiard with a…
We study analytically and numerically the classical diffusive process which takes place in a chaotic billiard. This allows to estimate the conditions under which the statistical properties of eigenvalues and eigenfunctions can be described…