Tunneling coherent

The coherent tunneling case is experimentally dealt with in spectroscopic studies. For example, the neutron-scattering structure factor determining the spectral line shape is... 

As long as the system can be described by the rate constant - this rules out the localization as well as the coherent tunneling case - it can with a reasonable accuracy be considered in the imaginary-time framework. For this reason we rely on the Im F approach in the main part of this section. In a separate subsection the TLS real-time dynamics is analyzed, however on a simpler but less rigorous basis of the Heisenberg equations of motion. A systematic and exhaustive discussion of this problem may be found in the review [Leggett et al. 1987]. 

It is noteworthy that the above rule connects two quite different values, because the temperature dependence of is governed by the rate constant of incoherent processes, while A characterizes coherent tunneling. In actual fact, A is not measured directly, but it is calculated from the barrier height, extracted from the Arrhenius dependence k T). This dependence should level off to a low-temperature plateau at 7 < This non-Arrhenius behavior of has actually been observed by Punnkinen [1980] in methane crystals (see fig. 1). A similar dependence, also depicted in fig. 1, has been observed by Geoffroy et al. [1979] for the radical... 

As seen from this table, the WKB approximation is reasonably accurate even for very shallow potentials. At 7 = 0 the hindered rotation is a coherent tunneling process like that studied in section 2.3 for the double well. If, for instance, the system is initially prepared in one of the wells, say, with cp = 0, then the probability to find it in one of the other wells is P( jn, t) = 5sin (2Ar), while the survival probability equals 1 — sin ( Ar). The transition amplitude A t), defined as P( + t) = A t), is connected with the tunneling frequency by... 

Segal D, Nitzan A, Davis WB, Wasielewski MR, Ratner MA (2000) Electron transfer rates in bridged molecular systems 2. A steady-state analysis of coherent tunneling and thermal transitions. J Phys Chem B 104( 16) 3817—3829... 

Up to now, no direct measurements of diffusion coefficients have been reported for any system that show the low-temperature upturn just described, and it may well be that for most systems involving hydrogen such effects would occur only at ultra-low temperatures and minuscule diffusion rates. Also, the impurities and imperfections always present in real materials might well trap nearly all the diffusant atoms at the low temperatures at which coherent transport might be expected in ideal material. However, a recent measurement by Kiefl et al. (1989) of the (electronic) spin relaxation rate of muonium in potassium chloride over a range of temperatures gives spectacular support to the concept of coherent tunneling at low temperatures. (See Fig. 6 of Chapter 15 and the associated discussion.)... 

This correlation function oscillates in real time, thus providing no rate constant, as expected for coherent tunneling. This reveals a deficiency of... 

The dynamics of tunneling rotation of hindered rotors interacting with intra- and intermolecular vibrations has received much less attention than structural studies. Such interactions shift and broaden tunneling spectral lines and, when temperature is raised, lead to transitions from coherent tunneling to thermally activated hopping. 

At T = 0 the hindered rotation is a coherent tunneling process like that studied in Section 2.3 for the double well. If, for instance, the system is initially prepared in pure state localized in one of the wells, then the density matrix in the coordinate representation is given by... 

In this thesis, we will focus on molecules as individual wires. It is, nevertheless, important to point out, that electron and energy transport in higher dimensional molecular materials (such as polymers or molecular crystals) is closely interconnected. Many of the mechanisms that have been discussed in this thesis, such as coherent tunneling, thermal hopping, Forster transfer, etc., are present in both the single-wire systems and in molecular materials. 

Figure 4 Best coherent tunneling fits to the ACWJ data.[9, 11] Left tight-binding FS, anisotropic-s-wave OP. Right van Hove (vH) states, variosu OP s.

B. Two Possible Mechanisms of Coherent Tunneling of the Repolarization of Hydrogen-Bonded Chain... 

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