Strong and weak coupling limits

In Equation 6.88, K0 is the equilibrium constant for the formation of the collision complex, (V) 2 is the electronic coupling, and F is the Franck-Condon factor. In contrast to the radiationless relaxation, the energy transfer process cannot be rationalized only in the limit of the strong and weak coupling limits shown in Figure 6.16. 

To facilitate comparison between this result and the simpler one in (4.30) for E Sj gj, we quote the limiting forms of the ground state energy of HqM for strong and weak couplings ... 

It can be easily seen that T >Tq, Tp>Tp in both limits of strongly and weakly coupled CDWs. Our reasoning is valid even if among the temperatures (6,7) only those characterizing the actual structural instabilities are consistent with the appropriate limit of the interchain coupling. 

In the weak-coupling limit unit cell a (, 0 7a for fra/u-polyacetylene) and the Peierls gap has a strong effect only on the electron states close to the Fermi energy eF-0, i.e., stales with wave vectors close to . The interaction of these electronic states with the lattice may then be described by a continuum, model [5, 6]. In this description, the electron Hamiltonian (Eq. (3.3)) takes the form ... 

Calculation of the Current in Limit of Strong and Weak Exchange Coupling between the Dot and the Leads... 

Many interesting results by the investigation of quantum transport in the strong electron-vibron coupling limit has been achieved with the help of the master equation approach [104,106-109]. This method, however, is valid only in the limit of very weak molecule-to-lead coupling and neglects all spectral effects, which are the most important at finite coupling to the leads. 

In the previous section we have dealt with a simple, but nevertheless physically rich, model describing the interaction of an electronic level with some specific vibrational mode confined to the quantum dot. We have seen how to apply in this case the Keldysh non-equilibrium techniques described in Section III within the self-consistent Born and Migdal approximations. The latter are however appropriate for the weak coupling limit to the vibrational degrees of freedom. In the opposite case of strong coupling, different techniques must be applied. For equilibrium problems, unitary transformations combined with variational approaches can be used, in non-equilibrium only recently some attempts were made to deal with the problem. [139]... 

However, in the preceding two decades, there have been many experimental discoveries, beside high-Tc superconductivity, evidencing that we do not have yet the proper theoretical skills and tools to deal well with strongly correlated electron systems. For instance, heavy-fermions, fractional quantum Hall effect, ladder materials, and very specially high-Tc superconductivity seem not accessible from the weak coupling limit. 

The theory of CDW and SDW instabilities has received much attention it differentiates between the weak-coupling limit (U intermediate-coupling limit [50,51,52], and the strong-coupling limit ( U>t) [35,53,54],... 

In equation (5), is the equilibrium constant for the outer-sphere association of the donor and acceptor, is the electronic transmission coefficient (the probability that products form once the nuclear configuration of the transition state is achieved), Vnu is the effective frequency for nuclear motion along the reaction coordinate in the neighborhood of the transition state, and the nuclear transmission coefficient nu is the classical exponential function of the activation energy. The weak-coupling limit corresponds to the limit in which Kei < 1, and for the strong-coupling limit /Cei = 1. 

When the donor and acceptor are sufficiently close, as in an ion pair or in covalently linked complexes, electron transfer can be promoted by the absorption of light. An absorption band corresponding to the light induced electron transfer is usnally called a charge transfer (CT) absorption band . The molecnlar parameters that determine the CT absorptivity, bandwidth, and band shape are the same molecular parameters that determine the magnitude of the electron-transfer rate constant.In the weak-coupling limit, the absorptivity of the CT absorption band is small (much less than 10 cm ) in the strong-... 

---