Strong coupling region

Fig. 13.2. Crossover diagram in the w — / plane (uncritical surface). The shaded parts indicate regions dominated by asymptotic power law behavior. Weak coupling region (/ < 1) Long dashes lines of fixed z (— 300 1, from above). Short dashes lines of fixed sfz (= 0,01 1, from above). Dotted lines of fixed s = (0-02 0,8, from above). In the strong coupling region a line of fixed z = 300 is shown...

We now turn to the domain / > 1. Clearly Eqs. (13.27) are stiO a valid representation of the RG mapping, and the scaling variables still take the form (13.23). However the strong coupling region is not connected to a 0-... 

In the strong-coupling region, the SDW response dominates, as expected from the result of 5 = 1 for the first-excited state (see Fig. 9). The decrease of the SCPO and SCPl responses can be understand in terms of the Lehmann representation of /P as... 

Let us start with ht A a Holstein model. In the strong-coupling region, it is usually the case to employ the Lang-Firsov transformation [80], defined as... 

Figure 2.27 (a) State Sj occupation probability as a function of time (b) energies of the and So states (strong coupling regions are indicated by circles) for an MMVB quasi-classical/Ehrenfest trajectory on azulene. (Adapted from Klein, S., Bearpark, M.J., Smith, B.R., Robb, M.A., Olivucci, M. and Bernardi, F., Chem. Phys. Lett, 292, 259-266, 1998.)... 

Ya or consider a channel count different from the maximum. For instance, when many channel maxima fall into regions of small q, where the adiabatic assumptions are likely to fail, one may decide to count channels as open if their potential remains below E until entering a strong coupling region defined by some q < qg. Also, the explicit inclusion of transitions between channels has been discussed as a possible variant of the SACM. ... 

Here in the strong coupling region, it is apparent that the magnitude of the displacement in the CT state can significantly affect the observed value of S. We note that in the adiabatic limit, the vibrational wavefunctions are anharmonic. However, for small vibrational quantum numbers, the wavefunctions can be approximated by linearly displaced oscillators with renormalized temperature dependent frequencies and displacements. A large S in the CT state can now appear to substantially increase the observed S value in the P band. 

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