Phonon-assisted tunneling mechanism

Dick [1977] explained this behavior within the framework of a phonon-assisted tunneling mechanisms using the TLS approximation and golden rule formalism (see Sections 2.3 and 6.4). One-phonon transitions dominate the mechanism at low temperatures, resulting in a linear dependence of k with 7 this follows directly from relation (6.27) when j3/Wl. At higher temperatures, the main contribution comes from Raman processes, leading to a T4 dependence of the rate constant. This predicted T4 temperature dependence for RbBr OH- is analogous to results obtained by Silbey and Trommsdorf [1990] for two-proton transfer in benzoic acid crystals (see Section 6.4). 

K. The transition time is 102 s at 1.3 K. Kapphan and Luty proposed a phonon-assisted tunneling mechanism for this process. Although the notion that a mass as heavy as Ag+ can tunnel 0.9 A through a 0.17-kcal/mol barrier at 1.3 K is quite surprising, the experimental data and analysis clearly support this conclusion. 

The dispersionless optical phonon mode />, splits the degenerated unperturbed electron level (j = 1,2) while the mode b2 mediates the electron transitions between the levels. This latter term represents phonon-assisted tunneling, a mechanism of the... 

A void structure of the type shown in Figure 5.13(a) may contain at the interior surfaces a high density of surface states. Phonon-assisted tunneling to these internal surface states may be the mechanism responsible for the tunneling characteristic such as that shown in Figure 5.24. Surface states often show a symmetric density distribution (Chiarotti et al (1971)) with Ep pinned at its center. 

Analysis [12] of the temperature dependences of the frequency distribution P io) and of the jump distribution P(A t) for individual chromophores provides what seems to be compelling confirmation of the above physical picture. (In the actual analysis of the data the expressions for P co) and P(A t) in Eqs. (15) and (21) were modified to include the effect of additional experimental noise [12].) For one chromophore the temperature dependence of the TLS flip rate is consistent with one-phonon-assisted tunneling, but for another it is not. More experimental studies on more molecules, for longer times, and over a wider range of temperatures, would help determine the mechanisms of TLS flipping, and would also provide further overall evidence to support (or refute) our picture. 

For g(x) to be proportional to 1/x, it requires the relaxation time to be an exponential function of some random variable such that x = xq exp ( ), where itself has a flat distribution. It means that ( ) = constant, and rt(x) = n ). (d /dx) oc x. If a, the polarisability, is also a function of then it can lead to a sub-linear frequency dependence of a (co). The functional form given for the variation of x can arise from two different relaxation mechanisms. The first is a classical barrier hopping, in which two energetically favourable sites like in a double well potential are separated by a barrier fV and = W/kT. The second mechanism is a phonon assisted quantum tunneling through a barrier, which separates two equilibrium positions, in which case = 2aR, where a is the localization length and R is the separation between the sites. In the first case, by treating JV as independent of R, it has been shown (Poliak and Pike, 1972) that... 

At energies near the electrons are confined to channels and are thus not typical three dimensional free electrons. But, we have ignored quantum mechanics and in reality the electrons can tunnel from one channel to another and between various allowed regions. Furthermore as already indicated if we allow the electrons to hop there will be an additional component due to thermally assisted processes (or phonon... 

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