Quantum Dynamics of Oblique Vibrational States in the Hénon-Heiles System

In this paper, we study the quantum time evolution of oblique non-stationary vibrational states in a Hénon-Heiles oscillator system with two dissociation channels. The oblique non-stationary states we are interested in are the eigenfunctions of the anharmonic zeroth-order Hamiltonian operator resulting from the transformation to oblique coordinates, which are defined as those coming from non-orthogonal coordinate rotations that express the matrix representation of the second-order Hamiltonian in a block diagonal form characterized by the polyadic quantum number $n = n_1 + n_2$. The survival probabilities calculated show that the oblique non-stationary states evolve within their polyadic group with a high degree of coherence up to the dissociation limits on the short time scale. The degree of coherence is certainly much higher than that exhibited by the local non-stationary states extracted from the conventional orthogonal rotation of the original normal coordinates. We also show that energy exchange between the oblique vibrational modes occurs in a much more regular way than the exchange between the local modes.