arXiv subjects

Holger Schanz

Publications and source records attributed to Holger Schanz.

39 records · Page 3Linked to original sources

arXiv1995

Quantization of Sinai's Billiard - A Scattering Approach

We obtained the spectrum of the Sinai billiard as the zeroes of a secular equation, which is based on the scattering matrix of a related scattering problem. We show that this quantization method provides an efficient numerical scheme, and its implementation for the present case gives a few thousands of levels without encountering any serious difficulty. We use the numerical data to check some approximations which are essential for the derivation of a semiclassical quantization method based also on this scattering approach.

chao-dyn↗

arXiv1995

Nonlinearity and trapping in excitation transfer: Dimers and Trimers.

We study the interplay between nonlinearity in exciton transport and trapping due to a sink site for the dimer and the trimer with chain configuration by a numerical integration of the discrete nonlinear Schroedinger equation. Our results for the dimer show, that the formation of a self trapped state due to the nonlinear coupling increases the life time of the exciton substantially. Self trapping can be enhanced by the sink for short times, but for long times it disappears. In the trimer consisting of a subdimer extended by a sink site exists a transition between states localized on the two sites of the subdimer before for larger nonlinear coupling self trapping on one site of the subdimer is observed. For large trapping rates the fear of death effect leads to an increasing life time of the excitation on both, the dimer and the trimer. The sink site is then effectively decoupled. We explain this effect using an asymptotic theory for strong trapping and demonstrate it by direct numerical computation.

chem-ph↗

arXiv1995

Semiclassical Quantization of Billiards with Mixed Boundary Conditions

The semiclassical theory for billiards with mixed boundary conditions is developed and explicit expressions for the smooth and the oscillatory parts of the spectral density are derived. The parametric dependence of the spectrum on the boundary condition is shown to be a very useful diagnostic tool in the semiclassical analysis of the spectrum of billiards. It is also used to check in detail some recently proposed parametric spectral statistics. The methods are illustrated in the analysis of the spectrum of the Sinai billiard and its parametric dependence on the boundary condition on the dispersing arc.

chao-dyn↗