Ultrafast Non-Adiabatic Dynamics of Molecular Systems

In this section, the density matrix method shall be applied to study the ultrafast dynamics of the system embedded in a heat bath. Due to the use of the ultrashort pulse in the pumping lasers the dynamic behaviors of both population and coherence have to be considered [1,19-21], 

To the second-order approximation, by using the Laplace transformation method, pblliw(t) can be eliminated from Eq. (3.55)  

Here it is assumed that yhMa ) denotes the real part of r a and the imaginary part of r a is included in cob ai). Similarly, 

Experimentally the dynamics of the product is also often measured. 

Notice that in (fp)avav only vibrational relaxation is involved due to the coupling between the system and the heat bath, i.e., [23-25] 

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