Quantum beats and chaos in the Hénon-Heiles Hamiltonian

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Abstract
The quantum density of states of the Hénon-Heiles Hamiltonian exhibits prominent low-frequency beats as a function of energy. We interpret the beats in terms of interferences of the three simplest isolated classical periodic orbits by a calculation of their amplitudes in the Gutzwiller trace formula. We show that periodic orbit theory can reproduce classically the main characteristics of the quantum beats. Both stable and unstable orbits contribute substantially in generating these long-range correlations, which coexist with the short-range fluctuations giving nearest-neighbor spacings distributions typical for chaos. With a Fourier analysis our conclusions confirm the quantum spectrum.