Periodic orbit theory in fractal drum

Research paper by Stefanie Russ, Jesper Mellenthin

Indexed on: 02 Feb '05Published on: 02 Feb '05Published in: Physics - Disordered Systems and Neural Networks


The level statistics of pseudointegrable fractal drums is studied numerically using periodic orbit theory. We find that the spectral rigidity $\Delta_3(L)$, which is a measure for the correlations between the eigenvalues, decreases to quite small values (as compared to systems with only small boundary roughness), thereby approaching the behavior of chaotic systems. The periodic orbit results are in good agreement with direct calculations of $\Delta_3(L)$ from the eigenvalues.