Related papers: Dynamical tunneling in mushroom billiards

We demonstrate that the free motion of any two-dimensional rigid body colliding elastically with two parallel, flat walls is equivalent to a billiard system. Using this equivalence, we analyze the integrable and chaotic properties of this…

We have measured resonance spectra in a superconducting microwave cavity with the shape of a three-dimensional generalized Bunimovich stadium billiard and analyzed their spectral fluctuation properties. The experimental length spectrum…

Analytically tractable dynamical systems exhibiting a whole range of normal and anomalous deterministic diffusion are rare. Here we introduce a simple non-chaotic model in terms of an interval exchange transformation suitably lifted onto…

We perform the first long-time exploration of the classical dynamics of a driven billiard with a four dimensional phase space. With increasing velocity of the ensemble we observe an evolution from a large chaotic sea with stickiness due to…

Sufficiently differentiable oval billiards always have invariant rotational curves, but there are only two types of ovals with an invariant horizontal circle in its phase-space: the constant width ovals and some very special symmetric…

We study some statistical properties for the behavior of the average squared velocity -- hence the temperature -- for an ensemble of classical particles moving in a billiard whose boundary is time dependent. We assume the collisions of the…

Statistical properties of energy levels and eigenfunctions in a ballistic system with diffusive surface scattering are investigated. The two-level correlation function, the level number variance, the correlation function of wavefunction…

We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…

The winning rule of billiards is to drive the billiard ball on the table into the designated holes. We try to study the trajectory of the billiard ball, so that we can predict the direction of the ball. For rational slopes, we got cutting…

The density of states for a chaotic billiard with randomly distributed point-like scatterers is calculated, doubly averaged over the positions of the impurities and the shape of the billiard. Truncating the billiard Hamiltonian to a N x N…

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 investigate the question of the rate of mixing for observables of a Z d-extension of a probability preserving dynamical system with good spectral properties. We state general mixing results, including expansions of every order. The main…

Systems of pinned billiard balls serve as simplified models of collisions, where all particles remain fixed in their positions while their (pseudo-)velocities evolve in accordance with the laws of conservation of energy and momentum. For…

We consider a slowly rotating rectangular billiard with moving boundaries and use the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be…

We present a dynamical analysis of a classical billiard chain -- a channel with parallel semi-circular walls, which can serve as a model for a bended optical fiber. An interesting feature of this model is the fact that the phase space…

We describe an exponential Fermi accelerator in a two-dimensional billiard with a moving slit. We have found a mechanism of trapping regions which provides the exponential acceleration for almost all initial conditions with sufficiently…

The seminal physical model for investigating formulations of nonlinear dynamics is the billiard. Gravitational billiards provide an experimentally accessible arena for their investigation. We present a mathematical model that captures the…

We construct a class of reflection laws for billiard processes in the unit interval whose stationary distribution for the billiard position and its velocity is the product of the uniform distribution and the standard normal distribution.…

Many classes of active matter develop spatial memory by encoding information in space, leading to complex pattern formation. It has been proposed that spatial memory can lead to more efficient navigation and collective behaviour in…

By a random billiard we mean a billiard system in which the standard specular reflection rule is replaced with a Markov transition probabilities operator P that, at each collision of the billiard particle with the boundary of the billiard…