Nearest-neighbor hoppings

Fig. 5. Illustration of nearest-neighbor hopping on a cubic network with different conductivities for the principal axes, the square-diagonals, and the cube-diagonals. The elemental conductivities have to be weighted by the number of possible paths and by the probability for a suitable orbital-overlap configuration.

In terms of the simplification of Eq. (1) defined by considering only nearest-neighbor hopping integrals (i.e., neglecting long-range hops), it can be shown (, that injected... 

The XXZ model is equivalent to a hard-core Bose-Hubbard model with only nearest-neighbor hopping and interaction. Recently the Bose-Hubbard model has been investigated, but exact phase diagrams have not been obtained so far in three or larger dimensions. It is hoped that DMFT will clarify the phase diagram in infinite dimensions. 

The description of excitation motion outlined in the previous sections assumes completely incoherent nearest neighbor hopping. This was treated in detail because it is the case of widest applicability especially with the materials of interest discussed in the final section. However, it should be noted that in some cases excitons can move coherently over several lattice spacings before being scattered i). For this case the diffusion coefficient is expressed in terms of the group velocity of the exciton v and the time between scattering events r. 

For nearest neighbor hops we know that = 1.13, and this may approach the value... 

In effect, we are dealing with a Hamiltonian like Eq. (3.1) with infinitely many states, N = The nearest-neighbor hopping matrix elements are A, and one can apply an external bias e, which induces a drift on the TB particle. In our simulations we have taken an ohmic spectral density (3.4) with a finite cutoff frequency ca. The two transport quantities of interest are the nonlinear mobility... 

We are interested in a situation where the extra particles in the lattice are described by a single band Hubbard Hamiltonian coupled to the acoustic phonons of the lattice as given in Equation 12.12 [ 128]. In the latter equation, the first and second terms describe the nearest-neighbor hopping of the extra-particles with hopping amplitudes J, and interactions V, computed for each microscopic model by band-structure calculations for Uj = 0, respectively. The third term is the phonon Hamiltonian. The fourth term is the phonon coupling obtained in lowest order in the displacement... 

The preceding derivation concentrates on one-dimensional nearest-neighbor hopping however, as noted by Murray,we can also have hopping in two or three dimensions. In the general situation we can write... 

It appears that the essential clue to solution of the problem of carrier motion along a conjugated chain is provided by the concept of defect-controlled motion in an ID system. It has been developed by Movaghar et al.(39) on the basis of Alexander et al. s (55) model of diffusion along an ID chain with nearest-neighbor hopping rates W distributed according to the function... 

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