Regular eigenstates

As discussed in Section IV B, statisticality results from the combined action of individual energy eigenstates, some of which lead to statistical behavior and others of which do not. The spatial correlation function approach64 focuses on properties of individual (stationary as well as nonstationary) quantum states and allows a unique labeling of quantum states as chaotic or regular, in a manner that links directly to both classical chaos as well as the statisticality of observables, such as reaction rates. 

In this case the doorway component of the total wavefunction determines the dissociation rates. Based on our previous discussion, we anticipate that the decay rates will fluctuate considerably for the regular states, since the relative magnitude of the doorway channel component is expected to vary drastically from one state to another. In contrast, chaotic states should have a more homogeneous representation of the doorway component. As a result, chaotic states yield a diminished sensitivity of the decay rate to the exact eigenstate studied. Furthermore, individual T, are expected to be insensitive to the identity of the doorway channel. 

Analysis of this 7feff using the techniques of nonlinear classical dynamics reveals the structure of phase space (mapped as a continuous function of the conserved quantities E, Ka, and Kb) and the qualitative nature of the classical trajectory that corresponds to every eigenstate in every polyad. This analysis reveals qualitative changes, or bifurcations, in the dynamics, the onset of classical chaos, and the fraction of phase space associated with each qualitatively distinct class of regular (quasiperiodic) and chaotic trajectories. 

The reference scattering state can be chosen as a distorted wave (with any level of distortion) or as a free wave, as long as it is regular at the origin and is an eigenstate of the asymptotic Hamiltonian, Ho — lirnH oo H Groenenboom et al... 

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