Investigations Of Anderson Localization Of Bose-Condensed Gas And It’s Dynamical Properties

Disordered quantum system plays a very important role in the field of Condensed Matter Physics. The research on Anderson localization properties of Bose condensation gas can help people further understanding about the characteristics and the formation mechanism of some disordered quantum phenomena. In this thesis, based on the nonlinear Gross-Pitaevskii equation, the Anderson localization of an interacting one-dimensional (1D) Bose-condensed gas in a disordered speckle potential and quasi-periodical optical lattice were studied by using Lagrange variation approach and split step Fourier methods. The main contents and the conclusions of this thesis are summarized as follows:Firstly, the basic concepts and the research status of the Anderson localization were introduced in chapter one. In order to facilitate the process of setting up and solving of the nonlinear dynamical equations of Bose-condensed gas, some related theories about Anderson localization was describes in detail in the second chapter. Meanwhile, the simulation method of disordered potential is also studied.Secondly, the one-dimensional Anderson localization of Bose-condensed gas in disordered potential is investigated. The results show that the Gaussian-like ansatz achieved good results in variation analysis. The relationship between the localization properties of Bose-condensed gas and the critical parameters of disorder system is obtained by solving G-P equations using analytical and numerical methods. And different Anderson localization features of Bose-condensed gas are obtained by changing the inter-atomic interaction, the strength of disorder and the characteristic intensity of speckle potential.Finally, the one-dimensional Anderson localization of interacting Bose-condensed gas in quasi-periodic optical lattices is studied. The results show that there is a crossover from extended states to localized states for increasing strength of disorder. And the turning point is named critical disorder strength. These results agree well with previous experiment conducted by G. Roati et al. In addition, the inter-atomic interaction is also having a significant impact on the Anderson localization properties of Bose-condensed gas. And the larger interaction between atoms goes against the formation of localization.