This paper studies the localization behaviour of Bose-Einstein condensates in disorder potentials, modeled by a Gross-Pitaevskii eigenvalue problem on a bounded interval. In the regime of weak particle interaction, we are able to quantify exponential localization of the ground state, depending on statistical parameters and the strength of the potential. Numerical studies further show delocalization if we leave the identified parameter range, which is in agreement with experimental data. These mathematical and numerical findings allow the prediction of physically relevant regimes where localization of ground states may be observed experimentally.

翻译：本文研究以Gross-Pitaevskii egenvalue问题为模型的闭合间隔的Bose-Einstein凝凝聚物在潜在障碍中的局部化行为。在微弱粒相互作用的体系下,我们可以根据统计参数和潜在潜力的强度,量化地面状态的指数化。数字研究进一步显示,如果我们离开与实验数据一致的已查明参数范围,则迁移就绪。这些数学和数字结果可以预测实际相关的制度,从而可以对地面状态进行实验性观测。