Spectral fluctuation properties of Hamiltonian systems: The transition region between order and chaos

The authors study numerically the classical dynamical behaviour, and the spectral fluctuation properties, of a class of Hamiltonian systems with two degrees of freedom. The quantum mechanical properties of these systems are monotonic but non-universal functions of the fraction of classical phase space filled by chaotic trajectories. It is found that the observed spectral fluctuation measures can be reproduced by a random-matrix model which depends on one parameter only.