Zener

Zhu I, Wdom A and Champion P M 1997 A multidimensional Landau-Zener description of chemical reaction dynamics and vibrational coherence J. Chem. Phys. 107 2859-71... 

Figure Bl.27.8. Schematic view of Picker s flow microcalorimeter. A, reference liquid B, liquid under study P, constant flow circulating pump and 2, Zener diodes acting as heaters T and T2, thennistors acting as temperature sensing devices F, feedback control N, null detector R, recorder Q, themiostat. In the above A is the reference liquid and C2is the reference cell. When B circulates in cell C this cell is the working cell. (Reproduced by pemiission from Picker P, Leduc P-A, Philip P R and Desnoyers J E 1971 J. Chem. Thermo. B41.)...

The Landau-Zener transition probability is derived from an approximation to the frill two-state impact-parameter treatment of the collision. The single passage probability for a transition between the diabatic surfaces H, (/ ) and R AR) which cross at is the Landau-Zener transition probability... 

The problem of branching of the wavepacket at crossing points is very old and has been treated separately by Landau and by Zener [H, 173. 174], The model problem they considered has the following diabatic coupling matrix ... 

Zener C 1932 Nonadiabatic crossing of energy levels Proc. R. Soc. A 137 696... 

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... 

This dependency is seen in the Landau-Zener expression for the probability of a classical particle changing states while moving through a non-adiabatic... 

In the study of (electronic) curve crossing problems, one distinguishes between a situation where two electronic curves, Ej R), j — 1,2, approach each other at a point R = Rq so that the difference AE[R = Rq) = E iR = Rq) — Fi is relatively small and a situation where the two electronic curves interact so that AE R) Const is relatively large. The first case is usually treated by the Landau-Zener fonnula [87-92] and the second is based on the Demkov approach [93]. It is well known that whereas the Landau-Zener type interactions are... 

All Np states belonging to the Pth sub-space interact strongly with each other in the sense that each pair of consecutive states have at least one point where they form a Landau-Zener type interaction. In other words, all j = I,... At/> — I form at least at one point in configuration space, a conical (parabolical) intersection. 

At this point, we make two comments (a) Conditions (1) and (2) lead to a well-defined sub-Hilbert space that for any further treatments (in spectroscopy or scattering processes) has to be treated as a whole (and not on a state by state level), (b) Since all states in a given sub-Hilbert space are adiabatic states, stiong interactions of the Landau-Zener type can occur between two consecutive states only. However, Demkov-type interactions may exist between any two states. 

Before we continue and in order to avoid confusion, two matters have to be clarified (1) We distinguished between two types of Landau-Zener situations, which form (in two dimensions) the Jahn-Teller conical intersection and the Renner-Teller parabolical intersection. The main difference between the two is... 

For the connection of this result to the well-known Landau-Zener formula [23] see [15]. 

Tully, J. C. Nonadiabatic Processes in Molecular Collisions. In Dynamics of Molecular Collisions, Part B (W.H. Miller, ed.). Plenum, New York (1976) Zener, C. Non-adiabatic crossing of energy levels, Proc. R. Soc. London, Ser. A 137 (1932) 696-702... 

C. Zener, Elasticity andAnelasticity of Metals, University of Chicago Press, Chicago, lU., 1948. 

The transition described by (2.62) is classical and it is characterized by an activation energy equal to the potential at the crossing point. The prefactor is the attempt frequency co/27c times the Landau-Zener transmission coefficient B for nonadiabatic transition [Landau and Lifshitz 1981]... 

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... 

Figure 3-46 The Zener diode controller supply regulator.

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