between the classical and quantum solutions. The values of the d.c. field $B_{dc}$ and drive frequency $\omega_0$ depend on the radius of the dot $R_0$ and certain other parameters. However, to give an idea of the magnitudes of the physical parameters involved, let us pick two representative points on the diagram: $({\tilde{\omega_c}},\epsilon)$ = (0.1, 0.1) corresponds to $\omega_0$ = 20 GHz and $B_{dc}$ = 20 gauss when $R_0 = 1\mu m$, while $\omega_0$ = 800 MHz and $B_{dc}$ = 0.08 gauss for $R_0 = 5\mu m$. Similarly, $({\tilde{\omega_c}},\epsilon)$ = (2.0, 2.0) corresponds to $\omega_0$ = 20 GHz and $B_{dc}$ = 800 gauss for $R_0 = 1\mu m$, while $\omega_0$ = 20 GHz and $B_{dc}$ = 32 gauss for $R_0 = 5\mu m$. The details of the these estimates are presented in Section V.

We analytically obtain conditions and look at various kinds of fixed points of the classical solutions. In section IV we study the spectral statistics of the quantum evolution operator, which shows clear signatures of the classical transition from quasi-integrabality to chaos. We also discuss the eigenfunctions properties in different regimes using the $\chi ^2$ distribution of $\nu$ freedoms as a convenient parameterization of the results. Then, we 