相关论文: Intermediate statistics in quantum maps

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity…

Triangular billiards whose angles are rational multiples of $\pi$ are one of the simplest examples of pseudo-integrable models with intriguing classical and quantum properties. We perform an extensive numerical study of spectral statistics…

We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical…

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…

We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and the resulting expression depends on 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…

For non-Hermitian equilateral q-pointed star-shaped quantum graphs of paper I [Can. J. Phys. 90, 1287 (2012), arXiv 1205.5211] we show that due to certain dynamical aspects of the model as controlled by the external, rotation-symmetric…

The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions,…

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…

Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…

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…

The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…

After surveying the quantum kinematics and dynamics of statistical transmutation, I show how this concept suggests a phase diagram for the two-dimensional matter in a magnetic field, as a function of quantum statistics. I discuss the…

We investigate the bottom of the spectra of infinite quantum graphs, i.e., Laplace operators on metric graphs having infinitely many edges and vertices. We introduce a new definition of the isoperimetric constant for quantum graphs and then…

The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…

The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their…

We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…

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…

We assume that the level spectra of quantum systems in the initial phase of transition from integrability to chaos are approximated by superpositions of independent sequences. Each individual sequence is modeled by a random matrix ensemble.…

We consider quantum graphs with spin-orbit couplings at the vertices. Time-reversal invariance implies that the bond S-matrix is in the orthogonal or symplectic symmetry class, depending on spin quantum number s being integer or…