Related papers: Statistical Properties of Quantum Graph Spectra
The form factor of a quantum graph is a function measuring correlations within the spectrum of the graph. It can be expressed as a double sum over the periodic orbits on the graph. We propose a scheme which allows one to evaluate the…
The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The…
We present exact, explicit, convergent periodic-orbit expansions for individual energy levels of regular quantum graphs. One simple application is the energy levels of a particle in a piecewise constant potential. Since the classical ray…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not…
We analyze a model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements. Under the condition of strong classical chaos and strong decoherence due to large coupling with the…
Curious spectral properties of an ensemble of random unitary matrices appearing in the quantization of a map p -> p+alpha, q -> q+f(p+alpha) in [Giraud et al. nlin.CD/0403033] are investigated. When alpha=m/n with integer co-prime m,n and…
We compare the statistical fluctuation properties of the baryon and meson experimental mass spectra with those obtained from theoretical models (quark models and lattice QCD). We find that for the experimental spectra the statistical…
We consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(tau) for these systems is evaluated semiclassically in terms of periodic and diffractive orbits. It is shown…
Quantum graphs are a paradigmatic model for quantum chaos as well as for spectral theory. We give a concise didactical introduction to quantum graphs, or Schr\"odinger Hamiltonians on metric graphs, with a focus on results related to…
It is well established numerically that spectral statistics of pseudo-integrable models differs considerably from the reference statistics of integrable and chaotic systems. In [PRL,93 (2004) 254102] statistical properties of a certain…
We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential…
We present an exact analytical solution of the spectral problem of quasi one-dimensional scaling quantum graphs. Strongly stochastic in the classical limit, these systems are frequently employed as models of quantum chaos. We show that…
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…
Statistical properties of evolving random graphs are analyzed using kinetic theory. Treating the linking process dynamically, structural characteristics such as links, paths, cycles, and components are obtained analytically using the rate…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory we derive numerical and in particular…
The statistics of the resonance widths and the behavior of the survival probability is studied in a particular model of quantum chaotic scattering (a particle in a periodic potential subject to static and time-periodic forces) introduced…
We consider the semiclassical ballistic sigma-model as an effective theory describing the quantum mechanics of classically chaotic systems. Specifically, we elaborate on close analogies to the recently developed semiclassical theory of…