Research On The Theory Of Landau-Zener Problems

Landau-Zener tunneling between energy levels is an important and fundamental quantum phenomenon. It exists in a variety of physical systems and has a very wide range of applications. In this thesis, the probability of Landau-Zener tunneling in various two-level systems has been studied. It importantly describes the time evolution operator method which is used of exact solution to Landau-Zener problems. The thesis has been divided into five chapters, and our works are included in the chapter 3.In chapter 1, the background of the research on Landau-Zener tunneling, the latest research progress as well as research significance are briefly described.In chapter 2, we review Zener tunneling model, then we discuss what is the Landau-Zener tunneling and analyze linear Landau-Zener model. Last, we describe the periodic modulation on the Landau-Zener tunneling.In chapter 3, we presented the method of time evolution operator for gaining Landau-Zener tunneling probability and analyzed how the probability changed with evolution time. We compared the time evolution operator method with those from other methods. It shows that this method is very simple.In chapter 4,we briefly describe the model of dissipative two-level system and the transition probability.In chapter 5, we give conclusions and some discussions and give briefly some good ideas about our next work.