function. This distribution is normalized and, by construction, has mean spacing $\langle{s}\rangle=1$. We recover the Poisson case taking $\nu =0$ and Wigner for $\nu =1$. A criticism to the Brody distribution is, however, that there is no first principles justification for its validity. The fact remains that it does fit the specific results found when considering explicit model systems. Results of the transition, as parameterized by $\nu$, are shown in Figure 5.

We also calculated higher-order eigenvalue spectral correlations[@bohigas1]. The average number of levels in an interval of length L is $<n(L)> = {1\over L}\sum_{\alpha< }n(\alpha ,L),$ where the $< >$ stands for spectral average, and $n(\alpha ,L)$ is the number of levels in an interval of length $L$ starting at $\alpha$ and ending at $\alpha +
L$. Also important are the various moments of the level distribution. The one considered here is the second moment of the average number of levels in a given stretch of length $L$ of the spectrum, the $\Sigma^2(L)$ statistic $$<\Sigma ^{2}(L)> = \left <(n(\alpha ,L) - <n(\alpha ,L)>)^2 \right >.$$ Another often calculated statistic is the Dyson-Mehta $\Delta _3(L)$ which measures the stiffness of the spectrum. This is defined by $${\Delta _3(L,\alpha )}={1\over L}{min_{A,B}}
