Molecular systems time-dependent observables

Figure 4(a) also demonstrates that laser pulses of finite duration tend to smooth out the details of molecular time-dependent observables. To give a representative example of the dependence of the pump-probe signals on the pulse duration. Fig. 4 compares pump-probe signals obtained for pulse durations (a) ti = T2 = 20 fs, (b) t =0, T2 = 20 fs, and (c) ti = T2 = 40 fs. It is interesting to note that impulsive preparation of the molecular system with a (5-function pulse (b) results only in minor changes of the pump-probe signal. This indicates that in the present case the impulsive limit is virtually achieved by resonant 20 fs pulses, as the pulse duration is shorter than the characteristic (e.g. vibrational) time scales of the molecular system. The... 

The RTD quantifies the number of fluid particles which spend different durations in a reactor and is dependent upon the distribution of axial velocities and the reactor length [3]. The impact of advection field structures such as vortices on the molecular transit time in a reactor are manifest in the RTD [6, 33], MRM measurement of the propagator of the motion provides the velocity probability distribution over the experimental observation time A. The residence time is a primary means of characterizing the mixing in reactor flow systems and is provided directly by the propagator if the velocity distribution is invariant with respect to the observation time. In this case an exact relationship between the propagator and the RTD, N(t), exists... 

While in the frequency domain all the spectroscopic information regarding vibrational frequencies and relaxation processes is obtained from the positions and widths of the Raman resonances, in the time domain this information is obtained from coherent oscillations and the decay of the time-dependent CARS signal, respectively. In principle, time- and frequency-domain experiments are related to each other by Fourier transform and carry the same information. However, in contrast to the driven motion of molecular vibrations in frequency-multiplexed CARS detection, time-resolved CARS allows recording the Raman free induction decay (RFID) with the decay time T2, i.e., the free evolution of the molecular system is observed. While the non-resonant contribution dephases instantaneously, the resonant contribution of RFID decays within hundreds of femtoseconds in the condensed phase. Time-resolved CARS with femtosecond excitation, therefore, allows the separation of nonresonant and vibrationally resonant signals [151]. 

---