NUMERICAL-STUDIES ON THE INTERACTIONS BETWEEN FERMI POLYADS - QUANTUMAND 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 use d for the second Fermi resonance Hamiltonian. Examination of the stati stical properties of the spectra showed that, when treated quantum mec hanically, this model differs substantially from random matrices becau se (i) the first Fermi resonance is integrable and its nondiagonal ter ms 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 exp ression and on the levels it connects. Computation of the largest Lyap unov exponent for trajectories in the classical phase space showed tha t the quantum and the classical systems behave similarly: the quicker a coupling Hamiltonian induces quantum chaos, the quicker the trajecto ries become unstable in the classical phase space.