Anharmonic modulation coupling

The experimental data was fitted, as shown in Fig. 5.10, to a convolution of this response function with the instrument response function. As the result, the decay time T-2/2 was estimated to be 1.1 0.1 ps. Recently, the population lifetime Ti of G-phonons was measured by incoherent time-resolved anti-Stokes Raman scattering and the lifetime was found to be 1.1-1.2 ps in semiconducting SWNTs [57]. Therefore, one can reasonably assume ipu Ti at room temperature. This result is consistent with the conventional Raman line width of semiconducting SWNTs [58]. The observed short lifetime of the G-phonons implies anharmonic mode coupling between G-phonons and RBM-phonons [59]. In fact, a frequency modulation of the G mode by the RBM has been reported, suggesting the anharmonic coupling between these vibrations [56]. 

Planck s constant as given in the appendix of Ch. 1, a value of 0.06 A is found for 8Qq. This value is not at all small and emphasizes the important geometrical consequence of the anharmonic modulation of the freqnency of by intermonomer modes (4). It gives a value of 0.017 A for 8Qq -8Qq (eq. (7.1)), a value close to 0.02 A, measured by electron diffraction. It shows that the theoretical description of the anharmonic coupling of and intermonomer modes of H-bonds, presented above, not only quite precisely reproduces spectra, but also reproduces such small geometrical effects, which are measured by completely independent methods. The experimentally verified correlation this theoretical description establishes between IR bandshapes and isotopic length variations 8Qq - 8Q° of H-bonds constitutes a strong snpport of its validity. Values of 8 - 5 can be in principle also measured by X-ray... 

The cornerstone of the strong anharmonic coupling theory relies on the assumption of a modulation of the fast mode frequency by the intermonomer distance. This behavior is correlated by many experimental observations, and it is undoubtly one of the main mechanisms that take place in a hydrogen bond. Because the intermonomer distance is, in the quantum model, represented by the dimensionless position coordinate Q of the slow mode, the effective angular frequency of the fast mode may be written [52,53]... 

The observation of novel quantum beats in the spectrally resolved fluorescence of anthracene21 forced one to consider, within the context of radiationless transition theory, the details of how IVR might be manifested in beat-modulated fluorescence decays. This work led to the concepts of phase-shifted quantum beats and restricted IVR,30a,4° and to a general set of results306 pertaining to the decays of spectrally resolved fluorescence in situations where an arbitrary number of vibrational levels, coupled by anharmonic coupling, participate in IVR. Moreover, three regimes of IVR have been identified no IVR, restricted (or coherent) IVR, and dissipative IVR.42... 

Finally, in t-stilbene there may be large off-diagonal anharmonic coupling matrix elements that can couple widely separated zero-order states. This can lead to less than ideal modulation depths. 

When qa=a /4 and with purely local anharmonic terms, the amplitude modulation becomes as favourable as the phase one due to the switching in of the Umklapp terms. Then even a small interchain anharmonic coupling stabilizes the phase modulation if it is repulsive, or leads to the lock-in of commensurate amplitude modulated configuration if it is attractive14.We have argued... 

Note that the simple and robust definition of the delta-funetion proposed by Krishna and Tully ° was used in the above expression, but this ehoiee is by no means restrictive. The anharmonicity and the intermode coupling of the vibrational states enter naturally the expression via the friction-like term, which modulates the strength of the non-... 

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