相关论文: Semiclassical Transition from an Elliptical to an …

A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflection from a boundary. For billiards in non-convex areas bounded by segments of confocal quadrics are studied. The topology…

The spectral statistics of the circular billiard with a point-scatterer is investigated. In the semiclassical limit, the spectrum is demonstrated to be composed of two uncorrelated level sequences. The first corresponds to states for which…

In the present note, we uncover a remarkable connection between the length of periodic orbit of a classical particle enclosed in a class of 2-dimensional planar billiards and the energy of a quantum particle confined to move in an identical…

This article is a part of a project investigating the relationship between the dynamics of completely integrable or close to completely integrable billiard tables, the integral geometry on them, and the spectrum of the corresponding…

Gutzwiller's semiclassical trace formula for the density of states in a chaotic system diverges near bifurcations of periodic orbits, where it must be replaced with uniform approximations. It is well known that, when applying these…

The classical Birkhoff conjecture claims that the boundary of a strictly convex integrable billiard table is necessarily an ellipse (or a circle as a special case). In this article we prove a complete local version of this conjecture: a…

Random-matrix theory is used to show that the proximity to a superconductor opens a gap in the excitation spectrum of an electron gas confined to a billiard with a chaotic classical dynamics. In contrast, a gapless spectrum is obtained for…

Billiard systems, broadly speaking, may be regarded as models of mechanical systems in which rigid parts interact through elastic impulsive (collision) forces. When it is desired or necessary to account for linear/angular momentum exchange…

The elliptical stadium is a plane region bounded by a curve constructed by joining two half-ellipses by two parallel segments of equal length. The billiard inside it, as a map, generates a two parameters family of dynamical systems. It is…

In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appropriate change of variables, can be rewritten as…

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…

The semiclassical formula for the coherent-state propagator is written in terms of complex classical trajectories of an equivalent classical system. Depending on the parameters involved, more than one trajectory may contribute to the…

We show that in the semiclassical limit, classically chaotic systems have universal spectral statistics. Concentrating on short-time statistics, we identify the pairs of classical periodic orbits determining the small-$\tau$ behavior of 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…

The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrability, namely integrability close to the boundary, and prove…

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…

An $S$--matrix approach is developed for the chaotic dynamics of a nonlinear oscillator with dissipation. The quantum--classical crossover is studied in the framework of the semiclassical expansion for the $S$--matrix. Analytical…

In this text we study billiards on ovals and investigate some consequences of a rotational symmetry of the boundary on the dynamics. As it simplifies some calculations, the symmetry helps to obtain the results. We focus on periodic orbits…

The methods of the high energy semiclassical quantization in the rational polygon billiards used in our earlier papers are generalized to an arbitrary rational multi-connected polygon billiards i.e. to the billiards which is a rational…

A way of construction of semiclassical wave function (SWF) based on the Maslov - Fedoriuk approach is proposed which appears to be appropriate also for systems with chaotic classical limits. Some classical constructions called skeletons are…