Kink trap

Fig. 7,3, Trapping of kink,- and Blocli front,- in tlie 1-tl medium. The coefficient 0 is set to = 5 and decreased to 0 = 1.8 inside the cetitrai region of widtii 300. Left Kink trap under the l l resonance, tlie same ]>arameters as in Fig. lb. Right Blodi front trap under tlie 2 1 resonance (B = 0.061, tlie same otlier parameters as in Fig. lb).

The dependence of the wave propagation direction on the coefficient /3 can be used to trap kinks and Bloch fronts. Such traps can be designed by creating spatial regions, where the coefficient j3 is locally changed to reverse the propagation velocity. The left pane in Fig. 7.3 shows an example of a kink trap in the oiie-dmiensioiial medinm at the 1 1 resonance. The value... 

Fig. 7,4. Trapping of kinks and Blocli fronts in the two-diniensional medium. The coefficient is set to = 5 and decreased to = 1.8 in the rectangiitar central region. The medium parainetei-s are the same as in Fig. 7.2. The system size is 1000 x 1000. Upper panek Kink trap in 1 1 resonance. The snapshots of the spatial distribution of Rctj are taken at t = 0000, t — 19000 and ( = 32000. Lower panel Bloch wave trap in 2 1 resonance. Snapshots the spatial distribution of Re>7 at t = 2000. ( = lOOOO and ( = 46800. (B = 0.061)...

Guinea [65J reports within the SSH model the scattering of neutral kinks with different initial velocities The kinks are trapped in bounce resonances" for small initial velocities, and above a certain threshold they bounce twice and separate to infinity with velocities significantly lower than the initial ones." Campbell et al. [101-103] report, within the (f)" model, kinks trapped in bounce resonances" for small initial velocities and above a certain threshold "n bounce collisions and separation to infinity" and narrow windows in which kinks are trapped in bounce resonances." These phenomena... 

Fig. 4. Illustrative model of paths between two trap sites embedded in a three-dimensional cubic lattice. The dashed 24-link line has 7 unnecessary kinks which reduce its contribution to the path sum, but there are many of them (Table 2) note that the kinks in the figure are two-dimensional but the count in Eq. 17 is three-dimensional. The paths corresponding to terms in Eq. 14 may in general cross over themselves and backtrack, but may not visit the initial or final sites twice. The latter condition does not arise directly from Eq. 13 but rather from the irreversibility concept underlying the theory of the rate constant...

Assume that the two sites are separated by N steps in the x-direction. (The formula can be straightforwardly generalized to arbitrary locations of the two trap sites.) The number of extra kinks in the path of length N > N is K, which is the number of pairs of non-essential steps. The formula given then follows from the combinatorials of N total steps which may be taken in any order, and which consist of six classes of objects, N + k, forward steps (in the -I- x direction), k, backward steps ( — x), ky sideways steps ( 4- y), ky sideways steps back ( — y), and k ( + z), and kj ( — z), where we must also have that k, H- ky 4- k = K. Asymptotically for large N > N the number of paths grows as 6 /N ... 

In the Gurney-Mott mechanism, the trapped electron exerts a coulombic attraction for the interstitial silver ion. This attraction would be limited to a short distance by the high dielectric constant of the silver bromide. Slifkin (1) estimated that the electrostatic potential of a unit point charge in silver bromide falls to within the thermal noise level at a distance of "some 15 interatomic spacings." The maximum charge on the sulfide nucleus would be 1 e. The charge on a positive kink or jog site after capture of an electron would not exceed e/2. An AgJ would have to diffuse to within the attraction range before coulombic forces could become a factor. 

An energy-level model for this mechanism, proposed hy Gerischer et al. [123], is shown in Fig. 30. The energy levels associated with Si - H2 groups at kink sites are assumed to be located just above the valence hand edge and hence sites for hole capture. A hole trapped at the kink site oxidizes one of the Si - H groups to release a... 

Shallow electron traps None Morphological sites with positive electron affinity (inverse kink, etc.)... 

Let us calculate the electron affinity (EA) and ionization potential (IP) of clusters of silver species adsorbed to virtual sites near the defect. These levels are shown for the positive kink in Figure 3 relative to their positions in the valence and conduction bands of the model. The EA has a sawtooth behavior but is larger than the AgBr EA for neutral clusters of all sizes up to 8 atoms. Thus, electron trapping will occur at clusters on the positive kink. Corresponding data for the negative and double kink are shown in Figure 4. 

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