Year: 2011
Type: article
Abstract: For a bounded domain whose boundary contains a number of flat pieces Γ i , i = 1, …, l we consider a family of non-symmetric billiards Ω constructed by patching several copies of Ω 0 along Γ i s. It is demonstrated that the length spectrum of the periodic orbits in Ω is degenerate with the multiplicities determined by a matrix group G . We study the energy spectrum of the corresponding quantum billiard problem in Ω and show that it can be split into a number of uncorrelated subspectra corresponding to a set of irreducible representations α of G . Assuming that the classical dynamics in Ω 0 are chaotic, we derive a semiclassical trace formula for each spectral component and show that their energy level statistics are the same as in standard random matrix ensembles. Depending on whether α is real, pseudo-real or complex, the spectrum has either Gaussian orthogonal, Gaussian symplectic or Gaussian unitary types of statistics, respectively.
Source: Nonlinearity
Author: Boris Gutkin
Institution: University of Duisburg-Essen
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1995509577