Hopping nearest neighbor

Another famous hopping model is Mott s variable range hopping [23], in which it is assumed that the localized sites are spread over the entire gap. At low temperatures, the probability to find a phonon of sufficient energy to induce a jump to the nearest neighbor is low, and hops over larger distances may be more favorable. In that case, the conductivity is given by... 

The 0-0 and H-H RDFs (not shown) indicate that no 0-0 or H-H covalent bonds are formed during the simulations at all densities. The g(Roti) shows a lattice-like structure at 115 GPa, which is consistent with proton diffusion via a hopping mechanism between lattice sites.65 At 34 GPa, the coordination number for the first peak in g(RQH) is 2, which indicates molecular H20. Between 95 GPa and 115 GPa, however, the coordination number for the first peak in g(RQH) becomes four, which indicates that water has formed symmetric hydrogen bonds where each oxygen has four nearest-neighbor hydrogens. 

Note also that the choice of what the move X- X from one phase space point to the next means microscopically depends on the type of problem that one wishes to study e.g., for a simulation of surface difiusion in the framework of the lattice gas model (see section 4.2), this move may mean a hop of a randomly chosen adatom to a randomly chosen nearest neighbor site (and W = 0 it this latter site is already taken). 

Figure 4 shows the calculated energy barrier for Mn and Co hopping through an octahedral face (F) into a nearest neighbor tetrahedron in the Li/vacancy layer at Xu = 0 and 1/2. This path is the first half Oh of the open Oh Td Oh path pictured... 

Above room temperature, the mobile 3 d electrons are well described by a random mixture of Fel" and FeB ions with the mobile electrons diffusing from iron to iron, some being thermally excited to FeA ions, but the motional enthalpy on the B sites is AH < kT. As the temperature is lowered through Tc, the Seebeck coefficient shows the influence of a change in mobile-electron spin degeneracy, and at room temperature the Seebeck coefficient is enhanced by correlated multielectron jumps that provide a mobile electron access to all its nearest neighbors. The electron-hopping time xi, = coi = 10" s... 

The fast-forward protocol can be used to assist an incomplete STIRAP population transfer via control of the time dependences of the phases of the fields. As a first example, we reconsider transfer of particles between sites of a linear lattice. In this example, the hopping rates, which connect nearest neighbor sites, are the analogs of the Stokes and Raman pulses in a conventional STIRAP. We now allow the hopping rates to change with time. The derivation of the fast-forward driving potential proceeds in the same manner as Section 3.3.5. The Schrodinger equation for an accelerated state T pp is... 

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.

---