Semiclassical Study of Statistical Measures of Spectral Fluctuations in Some Pseudointegrable Billiards

Details Semiclassical Study of Statistical Measures of Spectral Fluctuations in Some Pseudointegrable Billiards Semiclassical Study of Statistical Measures of Spectral Fluctuations in Some Pseudointegrable Billiards

2005-03-16

arxiv.org/abs/nlin/0503037v1

Nonlinear Sciences

Chaotic Dynamics

158 page, 44 figures Thesis(1999)

Scientific paper

Using semi-classical formalism and asymptotic proliferation law of periodic orbits, we obtain an analytical expressions for the two-level cluster function, spectral form factor, level spacing distribution and the number variance for pseudo-integrable billiards. Our analysis shows that these spectral fluctuation measures depend on two parameters as well as on the number of levels considered. These parameters are, (1) projected phase space area occupied by different classes of bands of periodic orbits and (2) length of the shortest periodic orbit characteristic of these classes.

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