Incoherent hopping

Ishizaki A, Fleming GR (2009) Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer reduced hierarchy equation approach. J Chem Phys 130 234111... 

The elastic contribution is also called elastic incoherent structure factor (EISF). It may be interpreted as the Fourier transformed of the asymptotic distribution of the hopping atom for infinite times. In an analogous way to the relaxation functions (Eq. 4.6 and Eq. 4.7), the complete scattering function is obtained by averaging Eq. 4.22 with the barrier distribution function g E) obtained, e.g. by dielectric spectroscopy (Eq. 4.5)... 

The experiments just discussed made it clear that the motion of the hole on the series of As represents a different mechanism of transport than tunneling. Giese [13] and Bixon and Jortner [18] suggested that this mechanism is incoherent hopping of the hole between neighboring bases. This means that the hole wavefunction is Hmited to one base. The wavefunctions of the remaining electrons on that base would of course be distorted by the presence of the hole. Thus in this view of the transport process the base on which the hole sits could be called a molecular polaron, or a small polaron because it is limited to one site. 

At temperatures when interstitial atoms and ions become mobile (typically, 20-30 K in both metals and insulators), they perform thermally-activated incoherent hops, the frequencies of which are exponentially dependent on reciprocal temperature ... 

Fig. 12.14. Schematic representation of charge transfer in a donor-DNA-acceptor system via a quantum-mechanical (QM) channel and via incoherent hopping according to Grozema et al. (1999, with permission)...

The structure of Eq. (7.22) is the same as that of Eq. (2.1). It determines the statistically averaged probability of incoherent transition at T>TC. Note that it is the interference of many waves that renders the transition incoherent. Formally below the crossover temperature this formula should describe the rate of the incoherent transitions from the ground state. However, the transition under these conditions should be coherent. This means that the incoherent hopping rate should vanish at 7 = 0. To take this fact into account Clough et al. [1982] calculated 1 statistically averaging (mn) - (m0) rather than mn). Their results show that this correction is significant only for low barriers and T TC. 

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