Related papers: Amplitude distribution of eigenfunctions in mixed …
We study the eigenstates of quantum systems with large Hilbert spaces, via their distribution of wavefunction amplitudes in a real-space basis. For single-particle 'quantum billiards', these real-space amplitudes are known to have Gaussian…
A statistical analysis of the eigenfrequencies of two sets of superconducting microwave billiards, one with mushroom-like shape and the other from the familiy of the Limacon billiards, is presented. These billiards have mixed…
Friedel oscillations of electron densities near step edges have an analog in microwave billiards. A random plane wave model, normally only appropriate for the eigenfunctions of a purely chaotic system, can be applied and is tested for…
Nonlinear coupling between eigenmodes of a system leads to spectral energy redistribution. For multi-wavespeed chaotic billiards the average coupling strength can exhibit sharp discontinuities as a function of frequency related to…
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…
Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate. Models that describe the multivariate…
We present a classical and quantum mechanical study of an Andreev billiard with a chaotic normal dot. We demonstrate that in general the classical dynamics of these normal-superconductor hybrid systems is mixed, thereby indicating the…
In this work we study the geometrical properties of the high-lying eigenfunctions (200,000 and above) which are deep in the semiclassical regime. The system we are analyzing is the billiard system inside the region defined by the quadratic…
High resolution eigenvalue spectra of several two- and three-dimensional superconducting microwave cavities have been measured in the frequency range below 20 GHz and analyzed using a statistical measure which is given by the distribution…
We present experimental results on the eigenfrequency statistics of a superconducting, chaotic microwave billiard containing a rotatable obstacle. Deviations of the spectral fluctuations from predictions based on Gaussian orthogonal…
This paper addresses the amplitude and phase dynamics of a large system non-linear coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the…
This paper studies the effects of distributed delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, conditions for amplitude death are obtained in…
Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical…
A transmission amplitude is considered for quantum or wave transport mediated by a single resonance coupled to the background of many chaotic states. Such a model provides a useful approach to quantify fluctuations in an established signal…
The exact probability distributions of the amplitudes of eigenfunctions, $\Psi(x, y)$, of several integrable planar billiards are analytically calculated and shown to possess singularities at $\Psi = 0$; the nature of this singularity is…
Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian Laplace eigenfunctions on the torus ("arithmetic random waves"). We study…
The experimentally measured multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We show that both these features can be used as additional…
We study the statistical properties of wavefunctions in a chaotic billiard that is opened up to the outside world. Upon increasing the openings, the billiard wavefunctions cross over from real to complex. Each wavefunction is characterized…
Contrary to prevailing notion we find that the spectrum associated with the extended states in a complex system may belong to the Poisson universality class if the system is subjected to a specific set of constraints. Our results are based…
We study a new statistics of wave functions in several chaotic and disordered systems: the random matrix model, band random matrix model, the Lipkin model, chaotic quantum billiard and the 1D tight-binding model. Both numerical and…