199 citations · 1.2k across the 28 of their papers we have counts for
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Geometrical theory of diffraction and spectral statistics
Martin Sieber
We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction…
Semiclassical Treatment of Diffraction in Billiard Systems with a Flux Line
Martin Sieber
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 s…
Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula
Martin Sieber
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 th…
Uniform Approximation for Period-Quadrupling Bifurcations
Martin Sieber, Henning Schomerus
We derive a uniform approximation for semiclassical contributions of periodic orbits to the spectral density which is valid for generic period-quadrupling bifurcations in systems w…
Bifurcations of Periodic Orbits and Uniform Approximations
Henning Schomerus, Martin Sieber
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 w…
Semiclassical Transition from an Elliptical to an Oval Billiard
Martin Sieber
Semiclassical approximations often involve the use of stationary phase approximations. This method can be applied when is small in comparison to relevant actions or action…
Uniform approximation for diffractive contributions to the trace formula in billiard systems
Martin Sieber, Nicolas Pavloff, Charles Schmit
We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional billiard systems with corners. This is achiev…
Semiclassical Quantization of Billiards with Mixed Boundary Conditions
Martin Sieber, Harel Primack, Uzy Smilansky +2
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 der…