Coherent tunneling mechanisms

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. 

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

The bridge-assisted electron transfer discussed above is a coherent quantum-mechanical process. Its tunneling nature is manifested by the exponentially... 

Aside from merely calculational difficulties, the existence of a low-temperature rate-constant limit poses a conceptual problem. In fact, one may question the actual meaning of the rate constant at r = 0, when the TST conditions listed above are not fulfilled. If the potential has a double-well shape, then quantum mechanics predicts coherent oscillations of probability between the wells, rather than the exponential decay towards equilibrium. These oscillations are associated with tunneling splitting measured spectroscopically, not with a chemical conversion. Therefore, a simple one-dimensional system has no rate constant at T = 0, unless it is a metastable potential without a bound final state. In practice, however, there are exchange chemical reactions, characterized by symmetric, or nearly symmetric double-well potentials, in which the rate constant is measured. To account for this, one has to admit the existence of some external mechanism whose role is to destroy the phase coherence. It is here that the need to introduce a heat bath arises. 

In this section we shall consider in some detail the mechanism of coherence breakdown due to the bath, in order to clarify the physical assumptions which underlie the concept of rate constant at low temperatures. The particular tunneling model we choose is the two-level system (TLS) with the Hamiltonian... 

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