Semiclassical regime

Classical behavior is expected to occur on time scales that are shorter than the Heisenberg time (3.4). As the energy of the initial wavepacket increases, the quasiclassical and semiclassical regimes will extend over longer time intervals if the level density increases, as is usually the case in bounded... 

Especially in the highly excited semiclassical regime the quantum properties and dynamics of atomic and molecular systems are most naturally discussed within the framework of chaos. Not only does chaos theory help to characterize spectra and wave functions, it also makes specific predictions about the existence of new quantum dynamical regimes and hitherto unknown exotic states. Examples are the discovery of frozen planet states in the helium atom by Richter and Wintgen (1990a) and... 

Since the phonon energy quantum hu> does not explicitly appear in both Eqs. 35 and 36, these formulas for the rate constant in the semiclassical regime should be derived without the single-mode model being relied on. That is, we should not neglect that various phonon modes contributing to the reaction coordinate Q have, in reality, various energy quanta. In this case, the phonon Hamiltonian in the reactant state (where the electron to be transferred is at the donor) consists of various normal modes. 

In the semiclassical regime, ET can take place only at fixed atomic positions. Therefore, electron transfer takes place only in the vicinity of Q Q. ... 

The Hamiltonian for the reactant-state potential in the multimode model is given by Eq. 37. In the semiclassical regime, both the coordinate r/, and its conjugate... 

In the semiclassical regime, the value of coordinate Q must be conserved on transition of an electron from the reactant and the product state under the Franck Condon principle. Since the diabatic potentials for these states are composed of multiple parabolas due to participation of large-energy-quantum intramolecular vibrations, the transition is specified by a simultaneous change in the quantum state of these vibrations, for example, from the wth state m r> in the reactant state to the... 

Second, calculations can be performed in a semiclassical regime, and the results plotted on a Poincare section in action-angle (I, 0) coordinates. Such diagrams may seem complicated (see figs. 10.16 and 10.17), but are at least in principle readily understood a near-horizontal line across the (1,0) plot corresponds to a torus in ordinary phase space. When periodically extended in the time coordinate, each line corresponds to a vortex tube embedded in the extended phase space of the periodically... 

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