相关论文: Scar functions in the Bunimovich Stadium billiard

We describe conditions under which higher-dimensional billiard models in bounded, convex regions are fully chaotic, generalizing the Bunimovich stadium to dimensions above two. An example is a three-dimensional stadium bounded by a cylinder…

We study the features of scarred eigenstates of relativistic neutrino billiards (NBs), graphene billiards (GBs) and Haldane graphene billiards (HGBs) and recapitulate those for nonrelativistic quantum billiards (NRQBs) with the shapes of a…

We compare the statistical properties of eigenvalue sequences for a gamma=1 Bunimovich stadium billiard. The eigenvalues have been obtained by two ways: one set results from a measurement of the eigenfrequencies of a superconducting…

Numerical calculations studying bound eigenstates in chaotic regions of phase space, including those of the stadium billiard, are summarized. These calculations demonstrate that the scars of periodic orbit model is seriously flawed. An…

Cosmological billiards arise as a map of the solution to the Einstein equations, when the most general symmetry of the metric tensor is implemented, under the BKL (named after Belinskii, Khalatnikov and Lifshitz) paradigm, for which points…

The dynamics of chaotic billiards is significantly influenced by coexisting regions of regular motion. Here we investigate the prevalence of a different fundamental structure, which is formed by marginally unstable periodic orbits and…

We apply the concept of Lagrangian descriptors to the dynamics on the Bunimovich stadium billiard, a 2D ergodic system with singular families of trajectories, namely, the bouncing ball and the whispering gallery orbits. They play a central…

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 this work we study the geometrical properties of the high-lying eigenfunctions (200,000 and above) which are deep in the semiclassical regime. The system we are analyzing is the billiard system inside the region defined by the quadratic…

In this note we further develop the idea of using a ``black box'' point of view (see our previous work) to study eigenfunctions for billiards which have rectangular components: they include the Bunimovich billiard, the Sinai billiard, and…

We extend the semiclassical theory of scarring of quantum eigenfunctions psi_{n}(q) by classical periodic orbits to include situations where these orbits undergo generic bifurcations. It is shown that |psi_{n}(q)|^{2}, averaged locally with…

We study the effect on quantum spectra of the existence of small circular disks in a billiard system. In the limit where the disk radii vanish there is no effect, however this limit is approached very slowly so that even very small radii…

Properties of a quantum mushroom billiard in the form of a superconducting microwave resonator have been investigated. They reveal unexpected nonuniversal features such as, e.g., a supershell effect in the level density and a dip in the…

We study the aspects of quantum chaos in mushroom billiards introduced by Bunimovich. This family of billiards classically has the property of mixed phase space with precisely one entirely regular and one fully chaotic (ergodic) component,…

We present an experimental setup based on the normal modes of vibrating soap films which shows quantum features of integrable and chaotic billiards. In particular, we obtain the so-called scars -narrow linear regions with high probability…

The superscars phenomena (Heller, E.J., Phys. Rev. Lett. 53, (1984) 1515) in the rational polygon billiards (RPB) are analysed using the high energy semiclassical wave functions (SWF) built on classical trajectories forming skeletons.…

Dynamical properties of the elliptical stadium billiard, which is a generalization of the stadium billiard and a special case of the recently introduced mushroom billiards, are investigated analytically and numerically. In dependence on two…

We discuss the localization of wavefunctions along planes containing the shortest periodic orbits in a three-dimensional billiard system with axial symmetry. This model mimicks the self-consistent mean field of a heavy nucleus at…

In the paper, we establish Squash Rigidity Theorem - the dynamical spectral rigidity for piecewise analytic Bunimovich squash-type stadia. We also establish Stadium Rigidity Theorem - the dynamical spectral rigidity for piecewise analytic…

We discuss the impact of recent developments in the theory of chaotic dynamical systems, particularly the results of Sinai and Ruelle, on microwave experiments designed to study quantum chaos. The properties of closed Sinai billiard…