Search PubMed⌕ Search

Biomedical subjects

C Schmit

Publications and source records attributed to C Schmit.

6 recordsLinked to original sources
PubMed2000

Spectral statistics of chaotic systems with a pointlike scatterer

The statistical properties of a Hamiltonian H0 perturbed by a localized scatterer are considered. We prove that if H0 describes a bounded chaotic motion, the universal part of the spectral statistics is not changed by the perturbation. This is done first within the random matrix model. Then it is shown by semiclassical techniques that the result is due to a cancellation between diagonal diffractive and off-diagonal periodic-diffractive contributions. The compensation is a very general phenomenon encoding the semiclassical content of the optical theorem.

Journal Article↗
PubMed2000

Diffractive corrections in the trace formula for polygonal billiards

We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional polygonal billiards. In polygons, diffraction typically occurs at the boundary of a family of trajectories. In this case the first diffractive correction to the contribution of the family to the periodic orbit expansion is of order of that of an isolated orbit, and gives the first sqrt[Planck's over 2pi] correction to the leading semiclassical term. Keller's geometrical theory of diffraction is inadequate for treating these corrections and we develop an alternative approximation based on Kirchhoff's theory. Numerical checks show that our procedure allows reduction of the typical semiclassical error by about two orders of magnitude. The method permits treatment of the related problem of flux-line diffraction with the same degree of accuracy.

Journal Article↗
PubMed2000

Gaussian unitary ensemble statistics in a time-reversal invariant microwave triangular billiard

The spectrum of a chaotic two-dimensional quantum billiard with threefold symmetry has been studied in an experiment with a superconducting microwave cavity. In total 622 eigenvalues were identified experimentally and compared with numerical calculations. The statistical analysis of the data shows that Gaussian unitary ensemble statistics can be observed for a spectrum of a time-reversal invariant system.

Journal Article↗