Dephasing mechanism

If the experimental lineshapes do not exhibit sub-bands and are asymmetric, or if they involve sub-bands, but with intensity anomalies with respect to the Franck-Condon progression law, then, together with the dephasing mechanism, damping of the slow mode ought to be also considered as occurring in a sensitive competitive way. 

This hyperfine broadening of resonant absorption is consistent with theoretical investigations according to which the main dephasing mechanism of magnetic molecules is connected to nuclear spins [52, 72-75]. 

The corresponding shape of the isotropic part of the spontaneous Raman band, computed by Fourier transformation of Lorentzian shape, while the line wings decay faster for a finite time scale of the dephasing mechanism. For the halfwidth of the band, on the other hand, only minor changes occur for variable rc. 

It should be possible to estimate r, the lifetime of the low-frequency Rh-C stretch using a2 and Am in Equation (5). The values for a2 = 1.2 THz and Am = 20 cm-1 yield a value for r of 0.75 ps. For a low-frequency mode that has a number of lower-frequency internal modes and the continuum of solvent modes to relax into, 0.75 ps is not an unreasonable value for the lifetime. A measurement of the Rh-C stretching mode lifetime would provide the necessary information to determine if the proposed dephasing mechanism is valid. In principle, the same mechanism will produce a temperature-dependent absorption line shift. However, other factors, particularly the change in the solvent density with temperature strongly influence the line position. Therefore, temperature-dependent line shifts cannot be used to test the proposed model. 

The vibrational echo results on HbCO in EgOH/H20 show an identical functional form of the temperature dependence as MbCO in the same solvent mixture. We therefore concluded that the same dephasing mechanisms active in Mb are also active in Hb. In both proteins, a power law, T13, is observed at low temperatures. This temperature dependence, observed in... 

The additional information in the Raman echo is even more important when multiple dephasing mechanisms might be operating simultaneously. 

Although the combination of echo and FID techniques can more precisely define the vibrational frequency perturbations w(t), connecting w(t) with the dynamics of the solvent and the solvent-vibration coupling requires a correct model of the dephasing mechanism. This section briefly reviews the potential dephasing mechanisms relevant to interpreting the experiments presented in Section IV. More comprehensive reviews can be found elsewhere (2,71). 

Figure 14 Raman-echo data (points) from the svm-rncthyl stretch in CH3CN show no change as T is increased. The solid curves are predicted from the FID data assuming fast modulation. Only fast dephasing mechanisms are operating the effects of slow density fluctuations are too small to observe. (Adapted from Ref. 3.)...

The bandwidth of the symmetric methyl stretch in ethanol-1,1-fib is unusually wide (15 cm 1) compared to other methyl-containing liquids, e.g., acetonitrile (6.5 cm-1) and methyl iodide (5.7 cm 1) (Table 1). (The deuteration prevents mixing of the methyl and methylene hydrogen vibrations.) Within the context of the dephasing ideas already presented, a number of possible reasons for this difference present themselves. However, a closer experimental examination of the system shows that none of these are correct, and a new dephasing mechanism must be considered (5). 

The combination of FID and echo experiments has eliminated all possibilities for pure dephasing mechanisms. Slow-modulation mechanisms are inconsistent with the echo results fast-modulation mechanisms are inconsistent with a broad line persisting at low temperature. Resonant... 

Figure 22 Raman-echo data (points) from the. vym-mcthyl stretch in CH3CD2OH in the liquid (295 K), in the high-temperature glass (80 K), and in the low-temperature glass (12 K). In all cases, there is no change in the decays between Ti = 0 and at Ti = 1 ps, showing that there is no slow dephasing mechanism. (Adapted from Ref. 5.)...

Table 2 Classification of Dephasing Mechanisms by Type of Intermolecular Potential, Type of Solvent Dynamics, and Speed of the Resulting Frequency Modulation...

The present study uses a quantum statistical method to show how the time-profile of CARS from molecules in liquids is associated with the inteimolecular dephasing mechanisms. Liouville space Feynman diagrams are used for the development of relevant transitions associated with pmrs of molecules. - The structure of the inteimolecular dephasing constant is clarified to identify the difference between the inteimolecular dephasing constant and intramolecular dephasing constant in Sec.ll. Section III presents the rovibrational interference mechanism. The sub-picosecond decay observed in CARS profile of neat benzene is explained in terms of this mechanism. 

Fj arises from a fourth-order interaction and is similar to F, except that an additional phonon is required making this channel less likely in most circumstances. F, and Fj are obviously population relaxation (T,) mechanisms but F3, which is also a fourth-order process, does not change the initial phonon population but modulates its frequency by exchange of two equal-frequency phonons on different phonon branches. Other, indirect, dephasing mechanisms have also been proposed, which rely on the modulation of the frequency shift terms via relaxation of the phonons involved in these terms. - ... 

The value of p is determined by the temperature dependence of the scattering rate of the dominant dephasing mechanism. 

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