Tunneling Hamiltonian

One can introduce the tunneling Hamiltonian in a second quantization formalism (39) which can be written in the form... 

In parallel, the related activity was in the field of single-electron shuttles and quantum shuttles [143-153]. Finally, based on the Bardeen s tunneling Hamiltonian method [154-158] and Tersoff-Hamann approach [159,160], the theory of inelastic electron tunneling spectroscopy (IETS) was developed [113-116,161-163],... 

Compare the tunneling Hamiltonian (54) and the tight-binding Hamiltonian (2), divided into left and right parts... 

For applications the tunneling Hamiltonian (54) should be formulated in the second quantized form. We introduce creation and annihilation Schrodinger operators c fc, cRk, (hq, cRq. Using the usual rules we obtain... 

The tunneling Hamiltonian includes rr-dependent matrix elements, considered in linear approximation... 

Now let us consider the polaron transformation (146)-(147) applied to the tunneling Hamiltonian... 

Now we see clear the problem while the new dot Hamiltonian (154) is very simple and exactly solvable, the new tunneling Hamiltonian (162) is complicated. Moreover, instead of one linear electron-vibron interaction term, the exponent in (162) produces all powers of vibronic operators. Actually, we simply remove the complexity from one place to the other. This approach works well, if the tunneling can be considered as a perturbation, we consider it in the next section. In the general case the problem is quite difficult, but in the single-particle approximation it can be solved exactly [98-101]. 

We can do some general conclusions, based on the form of the tunneling Hamiltonian (162). Expanding the exponent in the same way as before, we... 

The full Hamiltonian is the sum of the free system Hamiltonian H the intersystem electron-electron interaction Hamiltonian He, the vibron Hamiltonian Hy including the electron-vibron interaction and coupling of vibrations to the environment (dissipation of vibrons), the Hamiltonians of the leads Hr, and the tunneling Hamiltonian Ht describing the system-to-lead coupling... 

Our interest in quantum dot-sensitized solar cells (QDSSC) is motivated by recent experiments in the Parkinson group (UW), where a two-electron transfer from excitonic states of a QD to a semiconductor was observed [32]. The main goal of this section is to understand a fundamental mechanism of electron transfer in solar cells. An electron transfer scheme in a QDSSC is illustrated in Figure 5.22. As discussed in introduction, quantum correlations play a crucial role in electron transfer. Thus, we briefly describe the theory [99] in which different correlation mechanisms such as e-ph and e-e interactions in a QD and e-ph interactions in a SM are considered. A time-dependent electric field of an arbitrary shape interacting with QD electrons is described in a dipole approximation. The interaction between a SM and a QD is presented in terms of the tunneling Hamiltonian, that is, in... 

Here E is the energy of connection of a carrier with the 1th site Mj(q) = ue q where u is the dimensionless constant, which characterizes the degree of local deformation of the lattice by a carrier. The tunnel Hamiltonian (293) includes in addition the overlapping the phonon functions bqcpq(0) and b ( k 0) as we conjecture that the proton polaron engages in the lattice vibration as well (hence Tim becomes a function of the momentum q and/or k, too). In the present form, Eq. (293), the total number of phonons is not kept however, we imply that the phonons are absorbed and emitted by polarons and thus their total number remains invariable. Let us introduce the designation... 

As a result we find that in both the hydrogen and the deuterium case the ground state tunneling is describable by a pure spin tunnel Hamiltonian, which describes the tunnel splitting between the spatial pair of states of different symmetry. The implications are discussed in detail in Ref. [83]. 

Here, is the unity matrix of Hilbert space. In the case of the tunnel Hamiltonian it is simply... 

Sto 92Sto Notation of rotation- 2.6.4.2,191 tunneling Hamiltonian see [92Sto]. 

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