Related papers: Closed orbits and spatial density oscillations in …

Dynamical focusing of ensembles of neutral particles in energy and configuration space has been demonstrated recently [C. Petri et al. 2010, Phys. Rev. E (R) {\bf 82}, 035204] using time-dependent elliptical billiards. The interplay of…

A physically transparent and mathematically simple semiclassical model is employed to examine dynamics in the central-spin problem. The results reproduce a number of previous findings obtained by various quantum approaches and, at the same…

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,…

The impression gained from the literature published to date is that the spectrum of the stadium billiard can be adequately described, semiclassically, by the Gutzwiller periodic orbit trace formula together with a modified treatment of the…

We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and…

We study diffraction corrections to the semiclassical spectral density of dispersing (Sinai) billiards. They modify the contributions of periodic orbits (PO's), with at least one segment which is almost tangent to the concave part of the…

We classify the local bifurcations of one dov quantum billiards, showing that only saddle-center bifurcations can occur. We analyze the resulting planar system when there is no coupling in the superposition state. In so doing, we also…

In this paper, we study semilinear elliptic equations in domains where there is a natural class of solutions, which depend only on one variable, and whose simple geometry reflects the geometry of the domain. We prove that under quite…

Weyl's expansion for the asymptotic mode density of billiards consists of the area, length, curvature and corner terms. The area term has been associated with the so-called zero-length orbits. Here closed nonperiodic paths corresponding to…

Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate universal behaviour of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in…

Based on an accurate computation of the first 1851 quantal energy levels of the truncated hyperbola billiard, we have found an anomalous long-range modulation in the integrated level density. It is shown that the observed anomaly can be…

The orbit closure of the unfolding of every rational right and isosceles triangle is computed and the asymptotic number of periodic billiard trajectories in these triangles is deduced. This follows by classifying all orbit closures of rank…

We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in $\mathbb{R}^2$. This system is motivated by the dynamics of iterated…

The eigenvalues of the Hyperspherical billiard are calculated in the semiclassical approximation. The eigenvalues where this approximation fails are identified and found to be related to caustics that approach the wall of the billiard. The…

We consider the semiclassical theory in a joint phase space of spin and orbital degrees of freedom. The method is developed from the path integrals using the spin-coherent-state representation, and yields the trace formula for the density…

We study how the singular behaviour of classical systems at bifurcations is reflected by their quantum counterpart. The semiclassical contributions of individual periodic orbits to trace formulae of Gutzwiller type are known to diverge when…

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…

Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…

Densities of states weighted with the diagonal matrix elements of two operators A and B, i.e., rho^(A,B)(E) = sum_n <n|A|n><n|B|n> delta(E-E_n) cannot, in general, be written as a trace formula, and therefore no simple extension of…

We investigate the dynamics of a nonzero mass, circular orbit planet around an eccentric orbit binary for various values of the binary eccentricity, binary mass fraction, planet mass, and planet semi--major axis by means of numerical…