Dixon dip in the highly excited vibrational levels sharing a common approximate quantum number and its destruction under multiple resonances

It is demonstrated that Dixon dip can appear even for a set of quantum levels sharing a common approximate quantum number (the polyad number) corresponding to a resonance which is seriously perturbed by other complicated interactions, like in the simple systems of Henon–Heiles and quartic potentials. For the molecular systems of H2O and DCN with multiple resonances, this dynamical property will be destructed. Chirikov’s conjecture that overlapping of resonances will lead to chaos is discussed under this idea with an independent approach by the Lyapunov exponent analysis.