Periodic orbit theory in fractal drum

Details Periodic orbit theory in fractal drum Periodic orbit theory in fractal drum

2005-02-02

arxiv.org/abs/cond-mat/0502059v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

to appear in Physica A

Scientific paper

10.1016/j.physa.2005.05.064

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.

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