相关论文: Classical and Quantum Elliptical Billiards: Mixed …
Rigid bodies collision maps in dimension two, under a natural set of physical requirements, can be classified into two types: the standard specular reflection map and a second which we call, after Broomhead and Gutkin, no-slip. This leads…
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 study billiards in domains enclosed by circular polygons. These are closed $C^1$ strictly convex curves formed by finitely many circular arcs. We prove the existence of a set in phase space, corresponding to generic sliding trajectories…
This is the first survey of highly excited eigenstates of a chaotic 3D billiard. We introduce a strongly chaotic 3D billiard with a smooth boundary and we manage to calculate accurate eigenstates with sequential number (of a 48-fold…
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…
We describe a one-parameter family of dispersing (hence hyperbolic, ergodic and mixing) billiards where the correlation function of the collision map decays as $1/n^a$ (here $n$ denotes the discrete time), in which the degree $a \in (1,…
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.…
We report on the experimental study of the spectral properties of quantum systems consisting of two quantum billiards (QBs), one with chaotic, the other one with integrable classical dynamics, that are coupled to each other via an opening…
Avoided level crossings, commonly associated with quantum chaos, are typically interpreted as signatures of eigenstate hybridization and spatial delocalization, often viewed as ergodic spreading. We show that, contrary to this expectation,…
The boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius with the distance 2B between their centers, as introduced by Heller and Tomsovic in Phys. Today 46 38 (1993). We study two classical and…
We experimentally studied evolution of quasi-eigenmodes as classical dynamics undergoing a transition from being regular to chaotic in open quantum billiards. In a deformation-variable microcavity we traced all high-Q cavity modes in a wide…
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 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 present a computational scheme based on classical molecular dynamics to study chaotic billiards in static external magnetic fields. The method allows to treat arbitrary geometries and several interacting particles. We test the scheme for…
A hard-wall billiard is a mathematical model describing the confinement of a free particle that collides specularly and instantaneously with boundaries and discontinuities. Soft billiards are a generalization that includes a smooth boundary…
Billiard systems offer a simple setting to study regular and chaotic dynamics. Gravitational billiards are generalizations of these classical billiards which are amenable to both analytical and experimental investigations. Most previous…
In this work we study the nonlinear dynamics of the static and the driven ellipse. In the static case, we find numerically an asymptotical algebraic decay for the escape of an ensemble of non-interacting particles through a small hole due…
We present first measurements on a superconducting three-dimensional, partly chaotic microwave billiard shaped like a small deformed cup. We analyze the statistical properties of the measured spectrum in terms of several methods originally…
In standard (mathematical) billiards a point particle moves uniformly in a billiard table with elastic reflections off the boundary. We show that in transition from mathematical billiards to physical billiards, where a finite size hard…
We design a computational experiment in which a quantum particle tunnels into a billiard of variable shape and scatters out of it through a double-slit opening on the billiard's base. The interference patterns produced by the scattered…