of the model. These properties are obtained from a direct diagonalization of the one-period time evolution matrix. For the results presented here we vary the value of $\epsilon$ while keeping $J$, ${\tilde\hbar}$ and ${\tilde\omega_c}$ fixed, so as to go from the integrable to the chaotic regime in the phase diagram that coincide with the values considered in the classical case. We note that the appropriate RMT statistical ensemble is a COE rather than a CUE, because this model has a false-T breaking symmetry.

Next we discuss the RMT tests and their application to the results obtained for the QEE of our quantum dot model.

Nearest neighbor QEE distributions
----------------------------------

A local measure often used in RMT is the distribution of nearest-neighbor energy level separations, $P(s)$, where $s=\varepsilon_{n+1}-\varepsilon_n$. In the extreme integrable and chaotic regimes it has been established[@bohigas2; @jose] that $P(s)$ takes the Poisson or Wigner distribution forms, $$\label{eq:qee}
P_P(s) = e^{-s} \qquad {\rm and} \qquad
P_W(s) =  {\pi\over 2}\,s\,e^{-{\pi\over 4}s^2},$$ respectively. A convenient and often successful parameterization of the $P(s)$ obtained in the transition between $P_P$ to $P_W$ is provided by the Brody interpolation formula[@brody]: $$P_{\nu}(s) = \gamma(\nu+1)\,s^{\nu}\,\exp(-\gamma s^{\nu+1}),$$ where $\gamma = \left[\Gamma\left({\nu+2\over\nu+1}\right)\right]^
{\nu+1}$, and $\Gamma(x)$ is the Gamma 