Vibrational model, Frohlich

Figure 6. Vibrational states and representative photon-induced transitions for the set of vibrations a, wg. . . wk,. . . in the Frohlich vibrational model.

Figure 7. Formal representation of the interaction of an external EM field with the dissipative subsystem in the Frohlich vibrational model (n is the nonlinear coupling parameter (Equation 17) the other quantities have the same meaning as...

However, beyond this overt similarity, there are differences. For example, Covalon by the nature of covalency would have to operate under a much more stringent correlation than that existing in the Frohlich s model between one paired n-electron and all other such pairs along the chain. This is a natural consequence of distortion in the alternating single double bonds. This treatment also differs from that of self-consistent field treatment [19] of a linear chain and that of Little [20] in our inclusion of bond vibration. Covalon also differs from polaron treatments [21] in the consideration of the movement of spin-paired correlated electrons in a covalent bond, instead of movement of spin-uncorrelated electrons in the zeroth order. 

The prediction of the existence of a phenomenon analogous to a Bose-Einstein condensation, as in Frohlich s vibrational model, has been confirmed via several other approaches, namely, via a transport theory formalism by Kaiser and a molecular Hamiltonian approach by Bhaumik et and also by Wu and Austinthe basic concept has been shown to be on firm theoretical ground. The difficulty in these ideas gaining wide acceptance is the lack of conclusive experimental evidence to provide confirmation that such effects occur in biological membranes. Furthermore, the theory presented thus far is not at the stage where it can be used in an analytical sense to explain those data thus far reported or be used in a predictive manner. 

F. Kaiser, Boltzmann Equation Approach to Frohlich s Vibrational Model of Bose Condensation-Like Excitations of Coherent Modes in Biological Systems, Z. Naturforsch. 34a, 134 146. 

We shall call the frequency at which t = —2em and t" — 0 the Frohlich frequency coF the corresponding normal mode—the mode of uniform polarization—is sometimes called the Frohlich mode. In his excellent book on dielectrics, Frohlich (1949) obtained an expression for the frequency of polarization oscillation due to lattice vibrations in small dielectric crystals. His expression, based on a one-oscillator Lorentz model, is similar to (12.20). The frequency that Frohlich derived occurs where t = —2tm. Although he did not explicitly point out this condition, the frequency at which (12.6) is satisfied has generally become known as the Frohlich frequency. The oscillation mode associated with it, which is in fact the lowest-order surface mode, has likewise become known as the Frohlich mode. Whether or not Frohlich s name should be attached to these quantities could be debated we shall not do so, however. It is sufficient for us to have convenient labels without worrying about completely justifying them. 

In the Frohlich model (367), as in the Peierls transition and Kohn anomaly, the lattice vibration of wavevector Ikp produces a periodic variation in the lattice site positions. This new lattice periodicity results in an additional periodic... 

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