466 citations · 2.7k across the 81 of their papers we have counts for
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The Role of Diffraction in the Quantization of Dispersing Billiards
Harel Primack, Holger Schanz, Uzy Smilansky +1
We study diffraction corrections to the semiclassical spectral density of dispersing (Sinai) billiards. They modify the contributions of periodic orbits (PO's), with at least one s…
Quantization of Sinai's Billiard - A Scattering Approach
Holger Schanz, Uzy Smilansky
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 quant…
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…
Inside-Outside Duality for Planar Billiards -- A Numerical Study
Barbara Dietz, Jean-Pierre Eckmann, Claude-Alain Pillet +2
This paper reports the results of extensive numerical studies related to spectral properties of the Laplacian and the scattering matrix for planar domains (called billiards). There…
Quantization of the three dimensional Sinai billiard
Harel Primack, Uzy Smilansky
For the first time a three--dimensional (3D) chaotic billiard -- the 3D Sinai billiard -- was quantized, and high--precision spectra with thousands of eigenvalues were calculated.…