Decay mechanics, nonadiabatic quantum

Surface Hopping Model (SHM) first proposed by Tully and Preston [444] is a practical method to cope with nonadiabatic transition. It is actually not a theory but an intuitive prescription to take account of quantum coherent jump by replacing with a classical hop from one potential energy surface to another with a transition probability that is borrowed from other theories of semiclassical (or full quantum mechanical) nonadiabatic transitions state theory such as Zhu-Nakamura method. The fewest switch surface hopping method [445] and the theory of natural decay of mixing [197, 452, 509, 515] are among the most advanced methodologies so far proposed to practically resolve the critical difficulty of SET and the primitive version of SHM. 

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 S2 state shown in Fig. lb exhibits an initial decay on a timescale of 20 fs, followed by quasi-peiiodic recurrences of the population, which are... 

Let us first consider the population probability of the initially excited adiabatic state of Model 1 depicted in Fig. 17. Within the first 20 fs, the quantum-mechanical result is seen to decay almost completely to zero. The result of the QCL calculation matches the quantum data only for about 10 fs and is then found to oscillate around the quantum result. A closer analysis of the calculation shows that this flaw of the QCL method is mainly caused by large momentum shifts associated with the divergence of the nonadiabatic couplings F = We therefore chose to resort to a simpler approximation... 

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. 

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