Periodic orbits vibrograms

Figure 2 depicts the vibrogram corresponding to the dynamics on the ground state of iodine, modeled by a Morse potential with the equilibrium distance r = 2.67 A and the dissociation energy D = 12,542 cm 1 [14, 108]. The periodic orbit and its repetitions clearly appear in the vibrogram. The classical... 

The experimental vibrogram shows an important recurrence around 160 fs, which may be assigned to the edge periodic orbit (3,2°, -)n0rmai- Recently, the vibrogram analysis has been carried out by Michaille et al. [113] on the basis of another model proposed by Joyeux [118] as well as on an ab initio potential fitted to the experimental data of Pique [119]. Essentially the same classical periodic orbits appear in the different models at low energies. In the same context, let us add that Joyeux has recently applied the Berry-Tabor trace formula to a IF Fermi-resonance Hamiltonian model of CS2 [120] and carried out a classical analysis of several related resonance Hamiltonians [121]. 

Figure 4. Vibrogram of C2HD calculated with = 2000 cm-1 from all the vibrational energy levels predicted by the Dunham expansion corresponding to the Hamiltonian (3.12) obtained by Herman and co-workers by fitting to high-resolution spectra [112], The periods of the bulk periodic orbits of Table I obtained numerically for the classical Hamiltonian (3.12) are superimposed as circles. On the right-hand side, the main labels (n4,ns) of the periodic orbits are given.

Recurrences of Vibrogram of C2HD and Their Periodic-Orbit Assignment [112]... 

B. A. Hess Dr. Gaspard has introduced the vibrogram as a tool to extract periodic orbits from the spectrum by means of a windowed Fourier transform. This raises the question whether other recent techniques of signal analysis like multiresolution analysis or wavelet transforms of the spectrum could be used to separate the time scales and thus to disentangle the information pertinent to the quasiclassical, semiclassical, and long-time regimes. Has this ever been tried ... 

---