  Employing efficient diagonalization techniques, we perform a detailed
quantitative study of the regular and chaotic regions in phase space in the
simplest non-integrable atom-field system, the Dicke model. A close correlation
between the classical Lyapunov exponents and the quantum Participation Ratio of
coherent states on the eigenenergy basis is exhibited for different points in
the phase space. It is also shown that the Participation Ratio scales linearly
with the number of atoms in chaotic regions, and with its square root in the
regular ones.
