Zener model

The motivation comes from the early work of Landau [208], Zener [209], and Stueckelberg [210]. The Landau-Zener model is for a classical particle moving on two coupled ID PES. If the diabatic states cross so that the energy gap is linear with time, and the velocity of the particle is constant through the non-adiabatic region, then the probability of changing adiabatic states is... 

The physical description of strongly pressure dependent magnetic properties is the object of considerable study. Edwards and Bartel [74E01] have performed the more recent physical evaluation of strong pressure and composition dependence of magnetization in their work on cobalt and manganese substituted invars. Their work contrasts models based on a localized-electron model with a modified Zener model in which both localized- and itinerant-electron effects are incorporated in a unified model. Their work favors the latter model. 

This is, beyond all doubt, the most important process and the only one which has been already tackled with theoretically. Nevertheless, the prediction given by the classical overbarrier transition model is not correct for this collision [9] and the modified multichaimel Landau-Zener model developed by Boudjema et al. [34] caimot explain the experimental results for collision velocities higher than 0.2 a.u.. With regard to the collision energy range, we have thus performed a semi-classical [35] collisional treatment... 

The probability P in equations (61) and (62) may be related to the electronic coupling matrix element through equation (63) by application of the Landau-Zener model ... 

In the framework of the Landau-Zener model, P is related to H by means of equation (75). These equations are also valid when both the stretching and solvent reorganization coordinates are taken into account as in the case of dissociative electron transfer. 

Let us create a new Zener diode with a breakdown voltage of 3 volts. We will name this new Zener model Dz3V. The model parameter in PSpice that controls the breakdown voltage is called BV. Change the model as shown ... 

Section 6.5.1), two avoided crossings arise in Figure 6.10c at t = +10 fs between states /) and 1 3), the first of which is marked by a gray circle. Due to the highly nonadiabatic time evolution, diabatic transitions between these dressed states are likely to occur. The Landau-Zener model [48, 104, 105] estimates the probability for a diabatic transition at the avoided crossings as... 

Various models to compute the probability of hopping exist. One of the simplest is the Landau-Zener model for avoided crossings in a single coordinate. The probability of the hop is determined as... 

Limitations and refinements of the mean-field Zener model. 

In this section, theoretical foundations and application of the mean-field Zener model to III-V magnetic semiconductors are discussed in some detail. The capabilities of the model to describe various magnetic properties of (Ga,Mn)As are presented, too. In the final part, limitations of the model and its numerous refinements put recently forward are discussed. 

Gai. jMn.jAs. Furthermore, the scaling theory of electronic states near the MIT, discussed in the previous sections, makes it possible to explain the presence of the ferromagnetism on the both sides of the MIT, and a non-critical evolution of 7fc across the critical point (Matsukura et al. 1998b). A comparison between theoretical and experimental data in a wider range of Mn and hole concentrations requires reliable information on the hole density in particular samples, which is not presently available. In appears, however, that in the case of both Gai-jjMnjAs and Im jMnjAs on the insulator side of the MIT, the experimental values of Tc are systematically higher than those expected from the Zener model. 

Let a crossing of diabatic surfaces of potential energy occur in a certain point R0. Taking into account only the linear expansion term of the difference between the energies of the diabatic states near the crossing point (the Landau-Zener model)... 

Fig. 7. Cross-section for the charge exchange in H + H1 collisions [20]. The points are the experimental data. The line has been calculated using the Landau Zener model.

The probability of transition from one diabatic term to another when passing the point q, can be calculated using the Landau-Zener model [10]... 

Having considered the connection between the multiphoton resonances and the microwave threshold field for the K (n + 2)s —> (n,k) transitions, it is now interesting to return to the analogous n — n + 1 transitions which are responsible for microwave ionization and consider them from this point of view. We start with a two level description based on the extreme n and n + 1 m = 0 Stark states, a description which is the multiphoton resonance counterpart to the single cycle Landau-Zener model presented earlier. The problem is identical to the problem... 

Pillet et al. observed that adding small static fields dramatically reduces the microwave fields required for the ionization of Li.19 For example the application of a static field of 1 V/cm lowers the 15 GHz ionization threshold of the Li 42d state from 200 V/cm, to a broad threshold centered at 20 V/cm, a field only slightly in excess of E = 1/3n5 = 13 V/cm. The threshold field 200 V/cm corresponds to the hydrogenic threshold field of 1/9 n4, which will be described shortly. A small field has virtually no effect in a single cycle Landau-Zener model, but its dramatic... 

A (>0) is the electronic factor. 1-P is the probability for continuing on the lower PES, which corresponds to ET. If the barrier disappears, the Landau-Zener model should not be used and it may be necessary to include the nuclear coordinates in a wave packet model. 

We consider next the so-called Landau-Zener model that provides insight into non-adiabatic dynamics. The Landau-Zener model concerns the transition probability between two one-dimensional linear intersecting diabatic potentials... 

In the Landau-Zener model, dynamics is described by a single trajectory which due to the constant force undergoes an accelerated motion in the crossing region. The probability of a transition from diabatic state 1 to state 2 is denoted by P 2l which is also the probability of remaining in the lower adiabatic state, and the transition probability from the lower to the upper adiabatic state is then Pnonadia. = 1 — -P12, which is given by [16,17]... 

---