Recurrence relation periodic potentials

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 3 Absolute values of the autocorrelation functions used to calculate the spectra in Figure 4 for different values of AQ, given in the Figure. The initial drop of the autocorrelation is related to the slope of the potential energy surface directly below the excited state potential minimum. Recurrences occur at each vibrational period, independent of the value used for AQ.

The mechanisms of synchronous metastases are understood and are related to an early release of tumour cells with enough time for growth to gain imaging and potentially clinical relevance at the time of diagnosis. Recurrent or newly developed metastases are a common observation even years after effective treatment or resection of a primary tumour. Nevertheless, the mechanisms responsible for tumour cells becoming dormant but remaining viable to awake after an unpredictable period of time is not yet clarified (Leen 1999 Finlay and McArdle 1986 Leveson et al. 1985). 

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