Related papers: Chaotic dephasing in a double-slit scattering expe…
The statistics of energy levels of a rectangular billiard, that is perturbed by a strong localized potential, are studied analytically and numerically, when this perturbation is at the center or at a typical position. Different results are…
We study the motion of classical particles confined in a two-dimensional "nuclear" billiard whose walls undergo periodic shape oscillations according to a fixed multipolarity. The presence of a coupling term in the single particle…
We consider the motion of a particle subjected to the constant gravitational field and scattered inelasticaly by hard boundaries which possess the shape of parabola, wedge, and hyperbola. The billiard itself performs oscillations. The…
The exact and semiclassical quantum mechanics of the elliptic billiard is investigated. The classical system is integrable and exhibits a separatrix, dividing the phasespace into regions of oscillatory and rotational motion. The classical…
We investigate the influence that classical dynamics has on interference patterns in coherence experiments. We calculate the time-integrated probability current through an absorbing screen and the conductance through a doubly connected…
Random-matrix theory is used to show that the proximity to a superconductor opens a gap in the excitation spectrum of an electron gas confined to a billiard with a chaotic classical dynamics. In contrast, a gapless spectrum is obtained for…
We present an efficient method to solve scattering problems in two-dimensional open billiards with two leads and a complicated scattering region. The basic idea is to transform the scattering region to a rectangle, which will lead to…
We clarify from a general perspective, the condition for the appearance of chaotic energy spectrum in quantum pseudointegrable billiards with a point scatterer inside.
For classical billiards we suggest that a matrix of action or length of trajectories in conjunction with statistical measures, level spacing distribution and spectral rigidity, can be used to distinguish chaotic from integrable systems. As…
The study of electron motion in semiconductor billiards has elucidated our understanding of quantum interference and quantum chaos. The central assumption is that ionized donors generate only minor perturbations to the electron…
Quantum walks are at present an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior.…
In the present work we explore the concept of solitary wave billiards. I.e., instead of a point particle, we examine a solitary wave in an enclosed region and explore its collision with the boundaries and the resulting trajectories in cases…
Integrability of a square billiard is spontaneously broken as it rotates about one of its corners. The system becomes quasi-integrable where the invariant tori are broken with respect to a certain parameter, $\lambda = 2E/\omega^{2}$ where…
We analyze on a simple classical billiard system the onset of chaotical behaviour in different dynamical states. A classical version of the "nuclear billiard" with a 2D deep Woods-Saxon potential is used. We take into account the coupling…
We study the quantum behaviour of chaotic billiards which exhibit classically diffusive behaviour. In particular we consider the stadium billiard and discuss how the interplay between quantum localization and the rich structure of the…
Astute variations in the geometry of mathematical billiard tables have been and continue to be a source of understanding their wide range of dynamical behaviors, from regular to chaotic. Viewing standard specular billiards in the broader…
In the present note, we uncover a remarkable connection between the length of periodic orbit of a classical particle enclosed in a class of 2-dimensional planar billiards and the energy of a quantum particle confined to move in an identical…
We explore the critical parameters responsible for the transition from integrability to chaos in a family of billiards combining elliptical and oval deformations. Unlike standard oval billiards, where a known critical parameter governs the…
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…
We explore the effects of the proximity to a superconductor on the level density of a billiard for the two extreme cases that the classical motion in the billiard is chaotic or integrable. In zero magnetic field and for a uniform phase in…