Time-dependent population probability nonadiabatic quantum dynamics

Let us briefly discuss the characteristics of the nonadiabatic dynamics exhibited by this model. Assuming an initial preparation of the S2 state by an ideally short laser pulse. Fig. 1 displays in thick lines the first 500 fs of the quantum-mechanical time evolution of the system. The population probability of the diabatic state shown in panel (b) exhibits an initial decay on a timescale of w 20 fs, followed by quasi-periodic recurrences of the population, which are damped on a timescale of a few hundred femtoseconds. Beyond 500 fs (not shown) the S2 population probability becomes quasi-stationary, fluctuating statistically around its asymptotic value of 0.3. The time-dependent population of the adiabatic S2 state, displayed in panel (a), is seen to decay even faster than the diabatic population — essentially within a single vibrational period — and to attain an asymptotic value of 0.05. The finite asymptotic value of is a consequence of the restricted phase space of the three-mode model. The population Pf is expected to decay to zero for systems with many degrees of freedom. 

Figure 26. Time-dependent simulations of the nonadiabatic photoisomerization dynamics exhibited by Model III, comparing results of the ZPE-corrected classical mapping approach (dotted lines) and exact quantum calculations (full lines). Shown are the population probabilities P t) and of the initially prepared adiabatic (a) and diabatic (b) electronic state, respectively, as well as the probability Pcis t) that the system remains in the initially prepared cis conformation (c).

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