Zener limit

The problem of nonadiabatic tunneling in the Landau-Zener approximation has been solved by Ovchinnikova [1965]. For further refinements of the theory beyond this approximation see Laing et al. [1977], Holstein [1978], Coveney et al. [1985], Nakamura [1987]. The nonadiabatic transition probability for a more general case of dissipative tunneling is derived in appendix B. We quote here only the result for the dissipationless case obtained in the Landau-Zener limit. When < F (Xe), the total transition probability is the product of the adiabatic tunneling rate, calculated in the previous sections, and the Landau-Zener-Stueckelberg-like factor... 

It gives 1 and dir/Lz in the limit of large and small values of the Landau-Zener parameter, respectively. 

The Landau-Zener formula in the limit J2/ v - oo gives PLZ = 1 whereas Eq. (183) for the case of fast fluctuations in this limit gives P — At small values of J2/ u, both formulas give the same result, P = 2itJ2/ v. ... 

DR. MEYER Dr. Schatz has led me to believe in certain things, and I want to ask him a question. It occurs to me that the Landau-Zener equation cannot work except in the nonadiabatic limit. Do you have any comments on that ... 

DR. MARSHALL NEWTON (Brookhaven National Laboratory) The Landau-Zener theory in the weak-coupling regime may be derived by perturbation theory, as Dr. Sutin mentioned earlier. The complete derivation is much more general than the perturbation theory, and allows one to include an arbitrary degree of coupling. Thus, one can go continuously from nonadiabatic to the adiabatic limits. 

The Landau-Zener expression is calculated in a time-dependent semiclassical manner from the diabatic surfaces (those depicted in Fig. 1) exactly because these surfaces, which describe the failure to react, are the appropriate zeroth order description for the long-range electron transfer case. As can be seen, in the very weak coupling limit (small A) the k l factor and hence the electron transfer rate constant become proportional to the absolute square of A ... 

If you add a lot of series resistance - enough to limit the current heating - they behave like a ratty zener and can recover lots of times. You have to see what else happens when you add that much resistance - might destroy other needed features - or maybe it s tolerable. 

This circuit gives the user the option to use a DC current or to use a pulsed current as a load (useful for checking load-switching transients of power supplies). The 15 V input signal is dropped to 10 V by a 5 V zener in series. Switch A selects between the simple potentiometer voltage divider circuit (limited to 5 V maximum by the divider resistors)... 

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. 

Apart from separation considerations, Fig. 6.191 shows a very general principle in safety technology the principle of redundancy, in this case the doubling of components relevant to current and voltage limitation (resistors connected in series, Zener diodes in parallel). 

For voltage limitation, Zener diodes connected in parallel are generally used (see Fig. 6.204). They are protected against thermal overload by means of a fuse (in case of long-term overvoltage at the non-intrinsically safe side... 

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