Periodic orbit theory in fractal drum

Abstract

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.

to appear in Physica A

References in corpus (2)

• Level statistics and eigenfunctions of pseudointegrable systems: dependence on energy and genus number
• Periodic orbit theory and spectral rigidity in pseudointegrable systems