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

Abstract

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.