Related papers: Bouncing ball modes and quantum chaos
We present an extensive numerical study of spectral statistics and eigenfunctions of quantized triangular billiards. We compute two million consecutive eigenvalues for six representative cases of triangular billiards, three with generic…
We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to controversial issue of regular and irregular…
We give a beautiful explicit example of a convex plane curve such that the outer billiard has a given finite number of invariant curves. Moreover, the dynamics on these curves is a standard shift. This example can be considered as an outer…
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Several simple models of table motion are studied and compared. Dependence of displacement of the table on time,…
Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum…
Wave chaotic systems underpin a wide range of research activities, from fundamental studies of quantum chaos via electromagnetic compatibility up to more recently emerging applications like microwave imaging for security screening, antenna…
We investigate a quantum algorithm which simulates efficiently the quantum kicked rotator model, a system which displays rich physical properties, and enables to study problems of quantum chaos, atomic physics and localization of electrons…
We analyze the behavior of a gas of classical particles moving in a two-dimensional "nuclear" billiard whose multipole-deformed walls undergo periodic shape oscillations. We demonstrate that a single particle Hamiltonian containing coupling…
The classical and quantum dynamics of two ultra-strongly coupled and weakly nonlinear resonators cannot be explained using the Discrete Nonlinear Schr\"odinger Equation or the Bose-Hubbard model, respectively. Instead, a model beyond the…
We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of "quantum chaotic dynamics". It is shown that under quite general conditions their roots…
Billiards are flat cavities where a particle is free to move between elastic collisions with the boundary. In chaos theory these systems are simple prototypes, their conservative dynamics of a billiard may vary from regular to chaotic,…
We study transport through a two-dimensional billiard attached to two infinite leads by numerically calculating the Landauer conductance and the Wigner time delay. In the generic case of a mixed phase space we find a power law distribution…
A system of quantum computing structures is introduced and proven capable of making emerge, on average, the orbits of classical bounded nonlinear maps on \mathbb{C} through the iterative action of path-dependent quantum gates. The effects…
We illustrate some of the techniques to identify chaos signatures at the quantum level using as a guiding examples some systems where a particle is constrained to move on a radial symmetric, but non planar, surface. In particular, two…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball…
Semi--classical dynamics of quantum wave packets spreading is studied for a kicked rotor. Quantum flights are established for a specific, "magic" value of a chaos control parameter when the classical stickiness of trajectories is most…
We extended a previous qualitative study of the intermittent behaviour of a chaotical nucleonic system, by adding a few quantitative analyses: of the configuration and kinetic energy spaces, power spectra, Shannon entropies, and Lyapunov…
Several examples are known where quantum gravity effects resolve the classical big bang singularity by a bounce. The most detailed analysis has probably occurred for loop quantum cosmology of isotropic models sourced by a free, massless…
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…