Semiclassical Treatment of Diiraction in Billiard Systems with a Flux Line

Semiclassical treatment of diffraction in billiard systems with a flux line.

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 approximation for diffractive orbits that are scattered once on a flux line. This approximation is uniformly valid for all scattering angles. The diffractive contr...

ha o - dy n / 98 03 03 1 v 1 1 9 M ar 1 99 8 Bogomolny ’ s semiclassical transfer operator for rotationally invariant integrable systems

The transfer operator due to Bogomolny provides a convenient method for obtaining a semiclassical approximation to the energy eigenvalues of a quantum system, no matter what the nature of the analogous classical system. In this paper, the method is applied to integrable systems which are rotationally invariant , in two and three dimensions. In two dimensions, the transfer operator is expanded i...

Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula

We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index as an orbit is traversed. Results are given for isolated periodic orbits and rotationally invariant families of periodic orbits in axially symmetric billiard ...

Parametric evolution of eigenstates: beyond perturbation theory and semiclassics.

Considering a quantized chaotic system, we analyze the evolution of its eigenstates as a result of varying a control parameter. As the induced perturbation becomes larger, there is a crossover from a perturbative to a non-perturbative regime, which is reflected in the structural changes of the local density of states. The full scenario is explored for a physical system: an Aharonov-Bohm cylindr...

Semiclassical quantization of integrable and chaotic billiard systems by harmonic inversion