Temperature tunneling theory

Even Anderson et al. [39] pointed out that an important consequence of the tunnelling model was the (logarithmic) dependence of the measured specific heat on the time needed for the measurement of c. The latter phenomenon was due to the large energy spread and relaxation time of TLS. In 1978, Black [45], by a critic revision of the tunnelling theory, has been able to explain the time dependence of the low-temperature specific heat. 

J. T. Fermann and S. Auerbach, Modeling proton mobility in acidic zeolite clusters II. Room temperature tunneling effects from semiclassical theory, J. Chem. Phys. 112 (2000), 6787. 

This chapter is devoted to tunneling effects observed in vibration-rotation spectra of isolated molecules and dimers. The relative simplicity of these systems permits one to treat them in terms of multidimensional PES s and even to construct these PES s by using the spectroscopic data. Modern experimental techniques permit the study of these simple systems at superlow temperatures where tunneling prevails over thermal activation. The presence of large-amplitude anharmonic motions in these systems, associated with weak (e.g., van der Waals) forces, requires the full power of quantitative multidimensional tunneling theory. 

P. Pipinys and A. Kiveris, Analysis of temperature-dependent conductivity of nanotubular polyaniline on the basis of phonon-assisted tunneling theory, Physica B, 355,352-356 (2005). 

Here, is an effective overlap parameter that characterizes the tunneling of chaiges from one site to the other (it has the same meaning as a in Eq. (14.60)). T0 is the characteristic temperature of the exponential distribution and a0 and Be are adjustable parameters connected to the percolation theory. Bc is the critical number of bonds reached at percolation onset. For a three-dimensional amorphous system, Bc rs 2.8. Note that the model predicts a power law dependence of the mobility with gate voltage. 

Theoretically, the problem has been attacked by various approaches and on different levels. Simple derivations are connected with the theory of extrathermodynamic relationships and consider a single and simple mechanism of interaction to be a sufficient condition (2, 120). Alternative simple derivations depend on a plurality of mechanisms (4, 121, 122) or a complex mechanism of so called cooperative processes (113), or a particular form of temperature dependence (123). Fundamental studies in the framework of statistical mechanics have been done by Riietschi (96), Ritchie and Sager (124), and Thorn (125). Theories of more limited range of application have been advanced for heterogeneous catalysis (4, 5, 46-48, 122) and for solution enthalpies and entropies (126). However, most theories are concerned with reactions in the condensed phase (6, 127) and assume the controlling factors to be solvent effects (13, 21, 56, 109, 116, 128-130), hydrogen bonding (131), steric (13, 116, 132) and electrostatic (37, 133) effects, and the tunnel effect (4,... 

Among the theories of limited applicability, those of heterogeneous catalysis processes have been most developed (4, 5, 48). They are based on the assumption of many active sites with different activity, the distribution of which may be either random (23) or thermodynamic (27, 28, 48). Multiple adsorption (46, 47) and tunnel effects (4, 46) also are considered. It seems, however, that there is in principle no specific feature of isokinetic behavior in heterogeneous catalysis. It is true only that the phenomenon has been discovered in this category and that it can be followed easily because of large possible changes of temperature. 

The theory foresees the possibility of coulomb blockade phenomenon in such junctions. Averim and Likharev had investigated the conditions of vanishing for the Josephson tunneling and demonstrated the possibility of having normal electrodes in the junction. That is, no superconducting electrodes are necessary, and, therefore, coulomb blockade is possible to observe, in principle, even at room temperature. 

The requirement I > 2 can be understood from the symmetry considerations. The case of no restoring force, 1=1, corresponds to a domain translation. Within our picture, this mode corresponds to the tunneling transition itself. The translation of the defects center of mass violates momentum conservation and thus must be accompanied by absorbing a phonon. Such resonant processes couple linearly to the lattice strain and contribute the most to the phonon absorption at the low temperatures, dominated by one-phonon processes. On the other hand, I = 0 corresponds to a uniform dilation of the shell. This mode is formally related to the domain growth at T>Tg and is described by the theory in Xia and Wolynes [ 1 ]. It is thus possible, in principle, to interpret our formalism as a multipole expansion of the interaction of the domain with the rest of the sample. Harmonics with I > 2 correspond to pure shape modulations of the membrane. 

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