Coherent states generalized phase

Second, the mapping approach to nonadiabatic quantum dynamics is reviewed in Sections VI-VII. Based on an exact quantum-mechanical formulation, this approach allows us in several aspects to go beyond the scope of standard mixed quantum-classical methods. In particular, we study the classical phase space of a nonadiabatic system (including the discussion of vibronic periodic orbits) and the semiclassical description of nonadiabatic quantum mechanics via initial-value representations of the semiclassical propagator. The semiclassical spin-coherent state method and its close relation to the mapping approach is discussed in Section IX. Section X summarizes our results and concludes with some general remarks. 

The phase factor is unimportant here because we shall generally take the expectation value of any operator in the coherent state. 

Control of the type discussed above, in which quantum interference effects are used to constructively or destructively alter product properties, is called coherent control (CC). Photodissociation of a superposition state, the scenario described above, will be seen to be just one particular implementation of a general principle of coherent control Coherently driving a state with phase coherence through multiple, coherent,... 

Figure 7. Generalized phase coherent states. Wigner function for (5,0)p8j with different phase displacement parameters p chosen to be fractions of the quasiperiod T — 7 — 8.8.

It is generally believed that the relaxation of the phase coherence (dephasing) occurs on a shorter time scale than the time scale for the decay of excited state populations. For times much longer than the time scale for the loss of phase coherence, the generalized master equation is assumed to take the form of the kinetic equation... 

Generally, the recrystaUization of S-layer protein into coherent monolayer on phospholipid films was demonstrated to depend on (1) the phase state of the hpid film, (2) the nature of the lipid head group (size, polarity, and charge), and (3) the ionic content and pH of the subphase [122,138] (Table 6). 

A further important property of a MQC description is the ability to correctly describe the time evolution of the electronic coefficients. A proper description of the electronic phase coherence is expected to be particularly important in the case of multiple curve-crossings that are frequently encountered in bound-state relaxation dynamics [163]. Within the limits of the classical-path approximation, the MPT method naturally accounts for the coherent time evolution of the electronic coefficients (see Fig. 5). This conclusion is also supported by the numerical results for the transient oscillations of the electronic population, which were reproduced quite well by the MFT method. Similarly, it has been shown that the MFT method in general does a good job in reproducing coherent nuclear motion on coupled potential-energy surfaces. 

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