中文摘要：

通过数值方法产生一个随机函数来模拟实际的光斑电势，在准一维和弱无序情况下及对数坐标中，研究了囚禁在随机光斑电势中玻色-爱因斯坦凝聚（BEC）物质波的局域态及其稳定性和膨胀特性。结果发现，在无序存在和绝热条件下，物质波呈现出安德森定域化（AL）现象，并研究了弱的非线性空间调制对物质波AL的影响。

英文摘要：

By numerically solving the Gross-Pitaevskii equation, we advocate explorative studies of the formation and evolution of matter-wave characterized by Aderson localization （AL）, which is the issue of the considerable researches on Bose-Einstein condensate （BEC）. The random speckle potential is simula- ted with a random function produced by numeral methods. Starting from the quasi-one, dimensional Gross-Pitaevskii equation, we study the localization of a weakly interacting Bose-Einstein condensate trapped in a random speckle potential in logarithmic coordinates,under the condition of weak disorder. The stability and dilatation of localized states are investigated analytically by means of the split-step Fourier method,and the weak atomic interaction is modulated by controlling s-wave scattering length of Bose condensate atoms. Meanwhile, we also study the effects of the nonlinear spatial modulation on the shape, energy and localization length of the density envelope. The results show that there exists Ander- son localization in the presence of disorder and adiabatic condition due to the exponential tail. Remark- ably,it is found that the nonlinear spatial modulation has important influence on the energy, the central and tail region,and localization length of the localized states. Our results demonstrate some novel phe- nomena,opening up new means of matter-wave manipulation.