Related papers: Quantizing Billiards with Arbitrary Trajectories

The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions,…

We consider classical billiards in plane, connected, but not necessarily bounded domains. The charged billiard ball is immersed in a homogeneous, stationary magnetic field perpendicular to the plane. The part of dynamics which is not…

Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in a straight line on a (perfectly friction-less) table, striking the sides according to the law of reflection. A billiard trajectory is then…

Rational polygonal billiards are one of the key models among the larger class of pseudo-integrable billiards. Their billiard flow may be lifted to the geodesic flow on a translation surface. Whereas such classical billiards have been much…

We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although…

Because of a formal equivalence with the partition function of an Ising chain, the semiclassical traces of the quantum baker map can be calculated using the transfer-matrix method. We analyze the transfer matrices associated with the baker…

We investigate electron transport through clean open quantum dots (quantum billiards). We present a semiclassical theory that allows to accurately reproduce quantum transport calculations. Quantitative agreement is reached for individual…

We apply periodic-orbit theory to calculate the integrated density of states $N(k)$ from the periodic orbits of pseudointegrable polygon and barrier billiards. We show that the results agree so well with the results obtained from direct…

Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…

A general formula for the linearized Poincar\'e map of a billiard with a potential is derived. The stability of periodic orbits is given by the trace of a product of matrices describing the piecewise free motion between reflections and the…

This work explores the spectra of quantum graphs where the Schr\"odinger operator on the edges is equipped with a potential. The scattering approach, which was originally introduced for the potential free case, is extended to this case and…

Generic one-parameter billiards are studied both classically and quantally. The classical dynamics for the billiards makes a transition from regular to fully chaotic motion through intermediary soft chaotic system. The energy spectra of the…

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…

We extend the Gutzwiller trace formula to systems of noninteracting identical particles. The standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur…

The conductance through open quantum dots or quantum billiards shows fluctuations, that can be explained as interference between waves following different paths between the leads of the billiard. We examine such systems by the use of a…

Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum…

We extend the application of the concept of structural invariance to bounded time independent systems. This concept, previously introduced by two of us to argue that the connection between random matrix theory and quantum systems with a…

We establish a semiclassical trace formula in a general framework of microhyperbolic hermitian systems of $h$-pseudodifferential operators, and apply it to the study of the spectral shift function associated to a pair of selfadjoint…

We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum…

We study the influence of a tunnel barrier on the quantum transport through a circular cavity. Our analysis in terms of classical trajectories shows that the semiclassical approaches developed for ballistic transport can be adapted to deal…