Energy fluctuations of pseudointegrable systems with growing surface roughness.

Abstract

The eigenfrequencies of two-dimensional systems with fractal boundaries and with nonscaling rough boundaries are calculated numerically by the Lanczos algorithm and analyzed by means of level statistics. The systems are pseudointegrable and the fluctuations of their eigenvalue spectra show a global statistical behavior between the Poisson and the Wigner distributions. With increasing irregularity of the boundary, the systems approach the Wigner limit and the results seem to depend only on the genus number of the geometry and not on details, such as the asymptotic shape of the geometry, the type of roughness (scaling or nonscaling), and the boundary conditions (Neumann or Dirichlet). No transition between localized and extended states is found in fractal drums.