Effect Of Landau-Zener Tunneling By The Varying Sweeping Rate Of External Field

Landau-Zener tunneling between different levels, discovered by Landau, Zener and Stueckelberg in 1932, respectively, plays a basic and important role in quantum mechanics. This model describes the quantum tunneling between adjacent levels in a system driven by a outer field. Thus makes the tunneling effect can be found in variety of systems, such as spin system, chemical system, nucleon system. As a basic quantum phenomenon, it shows its versatile applications in collision theory, the spin tunneling of nanomagnets, BEC, field-driven superlattice, superconductor device and quantum computing. It has been 80 years since the Landau-Zener tunneling was found, but the physicists' attention in such area did not decrease. On the contrary, it increases much more because of the versatile applications for the theory.Landau-Zener Model is a simple and general theory about linear two-level tunneling, playing an important role in explaining many phenomena in physics. Based on the Landau-Zener tunneling theory, physicists developed the theory and made this theory applied in deeper areas in physics. For example, when linear two-level system extended to a nonlinear two-level system, a good model which help physicists to do research about the atoms in accelerating optical lattices appeared. In this ideal model, BEC system can be reduced to a two-level model is induced by the acceleration; the nonlinear Landau-Zener tunneling is the transition between two lowest Bloch bands. Some years later, some physicists show a theory which can dominate the Landau-Zener tunneling in a linear three-level system. Compare with the linear two-level systems. In this system, we can find that the properties in nonlinear system are similar with the ones in linear system if the nonlinearity is not strong enough. The only difference is the topological change on the mid-level. This topological structure change shows the adiabatic broken which manifests the presence of a nonzero tunneling probability. Meanwhile, unstable eigenstate can induce chaotic tunneling probability. While the strong nonlinearity makes topological distortions appear on the energy levels. The structure is so complicated that even break down the adiabatic theorem. This could help us to apply this theory to the three potential Bose-Einstein condensed systems because of the special properties. With the deeper physicists do the research, the wider the applications to use. Physicists extended the two-level, three-level to the many levels, and consider the more complicated problems with a time-varied sweeping rate or with a fast noise, from the outer environment. However, what our real interesting is the case of nonlinear Landau-Zener tunneling because this case owns some special properties. With the help of the research that physicists did, we get some general properties for the nonlinear tunneling probability. It can strangely change because the nonlinearity stronger and the broken symmetry.In this paper, we present the Landau-Zener tunneling theory and discuss the tunneling probability in different field and how the time-varied sweep rate infects the Landau-Zener tunneling probability. The structures are shown as follows:1. Introduce the discovery and progress in the studying of Landau-Zener tunneling.2. The simple models for describing Landau-Zener tunneling theory are presented. We introduce two-models to the Landau's adiabatic transition model and Zener's model.3. The behavior of two-level and three-level Landau-Zener tunneling is presented. We show the properties of Landau-Zener tunneling in linear driven fields and nonlinear driven fields, respectively.4. Discuss about how the nonlinearity of driven field infects the properties of Landau-Zener tunneling.5. Doing research the effect of Landau-Zener tunneling by the varying sweeping rate of external field.