Related papers: Power spectrum and form factor in random diagonal …
The fragmentation of diatomic molecules under a stochastic force is investigated both classically and quantum mechanically, focussing on their dissociation probabilities. It is found that the quantum system is more robust than the classical…
We studied the statistical properties of a quantum system in the pseudo-integrable regime through the gap ratios between consecutive energy levels of the scattering spectra. A two-dimensional quantum billiard containing a point-like…
Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry…
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 study the low-lying baryon spectrum (up to 2.2 GeV) provided by experiments and different quark models using statistical tools which allow to postulate the existence of missing levels in spectra. We confirm that the experimental spectrum…
We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2-$d$ quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic…
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…
This is a cursory overview of applications of concepts from random matrix theory (RMT) to quantum electronics and classical & quantum optics. The emphasis is on phenomena, predicted or explained by RMT, that have actually been observed in…
We calculate the eigenstates of a diatomic molecule in a range of model mean-field potentials, and evaluate the evolution of their associated Raman spectra with field strength. We demonstrate that dramatic changes in the appearance of the…
We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the…
Using a novel approach, we investigate the shape of the average spectrum and the spectral fluctuations of the $k$-body embedded unitary ensemble in the limit of large matrix dimension. We identify the transition point between semicircle and…
We consider $m$ spinless Fermions in $l > m$ degenerate single-particle levels interacting via a $k$-body random interaction with Gaussian probability distribution and $k <= m$ in the limit $l$ to infinity (the embedded $k$-body random…
We study matrix element fluctuations of the two-body screened Coulomb interaction and of the one-body surface charge potential in ballistic quantum dots, comparing behavior in actual chaotic billiards with analytic results previously…
In the present work the power spectrum of a particular class of tachyon fields is compared with the one corresponding to a cosmological constant model. This is done for different barotropic indexes $\gamma_0$ and the background space time…
We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations.…
We have investigated scaling properties of the Aubry-Andr\'e model and related one-dimensional quasiperiodic Hamiltonians near their localisation transitions. We find numerically that the scaling of characteristic energies near the ground…
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…
We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition…
We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulomb-interacting electrons. As such, the system resembles a prototype model for a semiconductor…
We propose a one-dimensional nonintegrable spin model with local interactions that covers Dyson's three symmetry classes (classes A, AI, and AII) depending on the values of parameters. We show that the nearest-neighbor spacing distribution…