Related papers: Numerical accuracy of Bogomolny's semiclassical qu…
In this paper, we show that two-dimensional billiards with point interactions inside exhibit a chaotic nature in the microscopic world, although their classical counterpart is non-chaotic. After deriving the transition matrix of the system…
A consistent scheme of semiclassical quantization in polygon billiards by wave function formalism is presented. It is argued that it is in the spirit of the semiclassical wave function formalism to make necessary rationalization of…
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,…
In billiard systems with a flux line semiclassical approximations for the density of states contain contributions from periodic orbits as well as from diffractive orbits that are scattered on the flux line. We derive a semiclassical…
The barrier billiard is the simplest example of pseudo-integrable models with interesting and intricate classical and quantum properties. Using the Wiener-Hopf method it is demonstrated that quantum mechanics of a rectangular billiard with…
We consider the semiclassical quantization of the Sinai billiard for disk radii R small compared to the wave length 2 pi/k. Via the application of the periodic orbit theory of diffraction we derive the semiclassical spectral determinant.…
We construct a semiclassically invariant function on the boundary of the billiard, taken as the Poincare section in Birkhoff coordinates, based on periodic orbit information, as an ansatz for the normal derivative of the eigenfunction.…
Ballistic transport through a collection of quantum billiards in undoped graphene is studied analytically within the conformal mapping technique. The billiards show pseudodiffusive behavior, with the conductance equal to that of a classical…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
We study the effect on the density of states in mesoscopic ballistic billiards to which a superconducting lead is attached. The expression for the density of states is derived in the semiclassical S-matrix formalism shedding insight into…
The Seba billiard, a rectangular torus with a point scatterer, is a popular model to study the transition between integrability and chaos in quantum systems. Whereas such billiards are classically essentially integrable, they may display…
A new algorithm for determining the eigenstates of n-dimensional billiards is presented. It is based on the application of the Cauchy theorem for the determination of the null space of the boundary overlap matrix. The method is free from…
The localization measures $A$ (based on the information entropy) of localized chaotic eigenstates in the Poincar\'e-Husimi representation have a distribution on a compact interval $[0,A_0]$, which is well approximated by the {\em beta…
We study classical and quantum scattering properties in the ballistic regime of particles in two-dimensional chaotic billiards that are models of electron- or micro- waveguides. To this end we construct the purely classical counterparts of…
We construct an autonomous chaotic Hamiltonian ratchet as a channel billiard subdivided by equidistant walls attached perpendicularly to one side of the channel, leaving an opening on the opposite side. A static homogeneous magnetic field…
Following the semiclassical formalism of Strutinsky et al., we have obtained the complete eigenvalue spectrum for a particle enclosed in an infinitely high spheroidal cavity. Our spheroidal trace formula also reproduces the results of a…
The present work consists of a numerical study of the dynamics of irrational polygonal billiards. Our contribution reinforces the hypothesis that these systems could be Strongly Mixing, although never demonstrably chaotic, and discuss the…
The paper is devoted to the derivation of random unitary matrices whose spectral statistics is the same as statistics of quantum eigenvalues of certain deterministic two-dimensional barrier billiards. These random matrices are extracted…
Harmonic inversion techniques have been shown to be a powerful tool for the semiclassical quantization and analysis of quantum spectra of both classically integrable and chaotic dynamical systems. Various computational procedures have been…
The pseudo-Euclidean Toda-like system of cosmological origin is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the ``singularity'' is reduced to a billiard on the…