NUMERICAL-STUDIES ON THE INTERACTIONS BETWEEN FERMI POLYADS - QUANTUM AND SEMICLASSICAL CHAOS

Numerical studies were performed for a system of two vibrational modes coupled by two Fermi resonances in order to investigate its classical and quantum chaotic behavior. Thirteen different expressions were used for the second Fermi resonance Hamiltonian. Examination of the statistical properties of the spectra showed that, when treated quantum mechanically, this model differs substantially from random matrices because (i) the first Fermi resonance is integrable and its nondiagonal terms cannot create level repulsion, spacing correlations, etc. and (ii) for the same value of the coupling strength, each coupling Hamiltonian has a different ability to induce quantum chaos, depending on its expression and on the levels it connects. Computation of the largest Lyapunov exponent for trajectories in the classical phase space showed that the quantum and the classical systems behave similarly: the quicker a coupling Hamiltonian induces quantum chaos, the quicker the trajectories become unstable in the classical phase space.