具有相互作用的无序玻色-爱因斯坦凝聚体
Disordered Bose Einstein Condensates with Interaction
摘要：
研究了Gross-Pitaevskii体系中单位区间上一维相互作用玻色子Lieb-Liniger模型中随机散射体对基态的影响。我们证明了玻色-爱因斯坦凝聚即使在散射体密度很高的强随机势下也能存在。然而，凝聚态的波函数的性质，在本质上取决于随机性和两体相互作用强度之间的相互作用。对于低密度的散射体或强相互作用，波函数扩展到整个区间。另一方面，散射体的高密度和弱相互作用导致波函数在间隔的碎片子集中的局部化。
英文摘要：
We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wave function of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers or strong interactions the wave function extends over the whole interval. High density of scatterers and weak interaction, on the other hand, leads to localization of the wave function in a fragmented subset of the interval.
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