Josephson Effects In The Bose-Einstein Condensation System

Recently, the Josephson effects of the Bose-Einstein Condensation (EEC) system have been the focus of considerable attraction. Their intrinsic nonlin-earity and the interaction with externally applied fields make them a kind of classical chaotic system. The known analytical method can predict the onset of some chaos in physical system, however, can't solve the nonlinear equations corresponding to chaotic system. The direct perturbation technique, proposed recently, successfully deals with a kind of perturbed chaotic system and obtains their formal solutions for each order. Those are what our paper is based on.This thesis consists of five parts. In the first chapter, introduction, we present the history and progress on regular and chaotic Josephson effects, also report the motivation and method about this paper. In the second chapter, on the basis of the work of Smerzi et al, we discuss the 7r-phase oscillations and the macroscopic quantum self-trapping effects under the symmetric time-independent well. The following chapter is on chaotic Josephson effects under the interaction between the BEG system and the laser. By use of the direct perturbation method, perturbed correction is construct and its boundedness conditions are established that contain the Melnikov criterion for the onset of chaos. Our numerical calculations reveal that the long-term oscillations of the system are not predictable. However, adjusting the initial conditions, we can suppress the inpredictability. In the fourth chapter, on the basis of the second and third chapter, using the Melnikov function approach, we find the conditions for producing chaotic Josephson effects and obtain the critertia for the chaos. In the fifth chapter, the brief summary and discussion of the work are given. The third and fourth chapter involve the author's partial original work.