Energy fluctuations of pseudointegrable systems with growing surface roughness - art. no. 056240

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 pseud ointegrable 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 l imit and the results seem to depend only on the genus number of the geometr y and not on details, such as the asymptotic shape of the geometry, the typ e of roughness (scaling or nonscaling), and the boundary conditions (Neuman n or Dirichlet). No transition between localized and extended states is fou nd in fractal drums.