Time-dependent observables, nonadiabatic quantum dynamics

The various aspects of photoinduced nonadiabatic dynamics are reflected by different time-dependent observables. Following a brief introduction of the observables of interest, we discuss how these quantities are evaluated in a mixed quantum-classical simulation. 

To perform a PO analysis of nonadiabatic quantum dynamics, we employ a quasi-classical approximation that expresses time-dependent quantities of a vibronically coupled system in terms of the vibronic POs of the system [123]. Considering the quasi-classical expression (16) for the time-dependent expectation value of an observable A, this approximation assumes that the integrable islands in phase space represent the most significant contributions to the dynamics of the observables considered [236]. As a consequence, the short-time dynamics of the system is determined by its shortest POs and can be approximated by a time average over these orbits. Denoting the A th PO with period 7 by qk t),Pk t) we obtain [123]... 

Then the recent notion of nonadiabaticity in electron d3mamics is introduced. To be consistent with the wavepacket bifurcation, we introduce the method of electron wavepacket d3mamics that undergoes bifurcation while being carried along the so-called non-Born-Oppenheimer paths, which also branch due to nonadiabatic interactions. We will further proceed to the discussion about the interaction of molecular nonadiabatic states with intense laser fields. In this way, we penetrate on one hand into unknown domains of molecular properties such as (1) electron-nuclear quantmn entanglement due to nonadiabatic transitions and its experimental observation, (2) coherence and decoherence of electron and nuclear wavepackets, which qualitatively dominate the quantmn mechanical probabiUties of quantum transition dynamics, (3) characteristic phenomena arising from the time-dependent fluctuation of molecular electronic states, (4) the physics of interference between the nonadiabatic djmamics and external fields, and so on. 

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