Coupling, strong, weak

The magnitude of the interaction is even more important than its nature, and it is thus convenient to make a distinction, as proposed by Forster, between three main classes of coupling (strong, weak and very weak), depending on the relative values of the interaction energy (U), the electronic energy difference between D and A (AE), the absorption bandwidth (Aw) and the vibronic bandwidth (As) (Figure 4.15). 

We prove our statement in two steps First, we consider the special case of a Hilbert space of three states, the two lowest of which are coupled strongly to each other but the third state is only weakly coupled to them. Then, we extend it to the case of a Hilbert space of N states where M states are strongly coupled to each other, and L = N — M) states, are only loosely coupled to these M original states (but can be stiongly coupled among themselves). 

Fig. 4.15. Distinction between strong, weak and very weak coupling.

Couple Strongly acid solutions Standard potentials (V) in Weakly acid solutions Neutral and basic solutions... 

Viewed in the time domain, the replacement of M(a>) by M washes out the details of the time variation within Q space. For this approximation to be useful, all strongly coupled states should be included in the P space and the Q space should not include any states that couple strongly to the P space (weak coupling assumption). We now find that the population dynamics of the m levels within the P space is governed by the equations of motion... 

If the mechanical degrees of freedom are coupled strongly to the environment (dissipative vibron), then the dissipation of molecular vibrations is determined by the environment. However, if the coupling of vibrations to the leads is weak, we should consider the case when the vibrations are excited by the current flowing through a molecule, and the dissipation of vibrations is also determined essentially by the coupling to the electrons. Here, we show that the effects of vibron emission and vibronic instability are important especially in the case of electron-vibron resonance. 

According to the value of S relative to the exciton bandwidth B, the relaxed form of the exciton will be delocalized or localized for — B < — S or — S < — B, respectively. Adopting Toyozawa s terminology,53 we can say that for S < gcB the exciton-phonon coupling is weak and for S > g(B it is strong, where gc is a characteristic parameter of the lattice structure of the order of unity (gc = 0.87 for the square lattice53). 

Figure 7.12 Energy diagrams for surface-molecule interactions in the case of (a) strong electronic coupling, (b) weak electronic coupling, and (c) no electronic coupling. ek stands for an electronic continuum of the metal or semiconductor band, whereas , represents the energy of frontier molecular orbital involved in this interaction...

Because signal 7 is further coupled to 6, which in turn is coupled strongly to 10 and weakly to 2, we can complete the assignments ... 

If the lectro phonon coupling is weak ( g <<1 for all q), the Hamiltonian may be used directly to study transport, as in section III. If the coupling is strong, the Hamiltonian is transformed to yield a weaker coupling as in section IV. In either case, the Hamiltonian is written... 

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