Time-dependent view Recurrences

In this section we consider indirect photodissociation of systems with more than one degree of freedom in the time-dependent approach. We will use the results of Section 7.2 to derive approximate expressions for the wavepacket evolving in the upper electronic state, the corresponding autocorrelation function, and the various photodissociation cross sections. 

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Figure 2 Time-dependent view of the luminescence transition in Figure 1. Only the potential energy curve of the final state is shown. Time-dependent wave functions are given for times of 0,10, and 50 fs. The bottom panel shows the absolute value of the autocorrelation function, visualized as the overlap between the time-dependent wavefunction (t) and the wavefunction at time zero. The first recurrence at 95 fs occurs after a single vibrational period of the 350 cm vibrational frequency used to define the harmonic potential energy curve.

The main characteristics of indirect dissociation are resonances in the time-independent picture and recurrences in the time-dependent approach. Resonances and recurrences are the two sides of one coin they reveal the same dynamical information but provide different explanations and points of view. To begin this chapter we discuss in Section 7.1, on a qualitative level, indirect photodissociation of a one-dimensional system. A more quantitative analysis follows in Section 7.2. The time-dependent and the time-independent views of indirect photodissociation are outlined and illustrated in Sections 7.3 and 7.4, respectively, with emphasis on vibrational excitation of the NO moiety in the photodissociation of CH30N0(S i). Section 7.5 accentuates the relation between... 

The time-dependent theoretical point of view provides a simple interpretation of the repetitive pattern. In the time domain, the overlap as a function of time for a given mode oscillates. The separation between the recurrences is a vibrational period. The total overlap is the product of the overlaps of each... 

From a time-dependent point of view, recurrences in the probability of occupying the initially prepared state give rise to the fine structure in the overtone absorption spectrum. Though rudiments of these recurrences may be present in the short-time trajectory P n,t), chaotic classical motion destroys the longer time recurrences, which occur quantum mechanically. It is these latter recurrences which are needed to evaluate fine details in the absorption spectrum. Thus, the classical trajectory method may be limited to the evaluation of low-resolution absorption spectra. However, it should be pointed out that progress is being made in extracting information from systems with... 

From the point of view of modeling the temporal behavior of earthquakes, the recurrence models can be divided in two main classes. The first class contains the memoryless model, i.e., the Poisson model, whereas the second class includes the non-Poissonian models, i.e., time-dependent models. While the Poisson model is extensively used in PSHAs, its adequacy is limited since the mechanism of earthquake interactions at regional scale has highlighted the tendency to a spatiotemporal clustering of earthquake occurrence, even for moderate earthquakes. Moreover, due to the memoryless ... 

In this article, a new point of view on the spectroscopic determination of potential surfaces is presented. The perspective is explicitly time dependent, although the theory given here is intended for interpretation of experiments in the frequency domain. We will travel back and forth between the time and frequency domains via Fourier transforms. Some of the characteristics of potential surfaces which we obtain are static ones, such as slopes and directions of excited (in absorption) or ground (in emission) potential surfaces in the Franck-Condon region. Other characterisitics are dynamic ones, involving certain decay and recurrence events which severely limit the form the potential surfaces may take but do not specify it completely. 

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