Bose-Einstein Condensation in the Luttinger-Sy Model
Bose-Einstein Condensation in the Luttinger-Sy Model
复制标题
Luttinger-Sy 模型中的玻色-爱因斯坦凝聚
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
V. Zagrebnov
中科院分区：
文献类型：
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作者：
O. Lenoble;V. Zagrebnov
我们提出了一个严谨的研究玻色-爱因斯坦凝聚在Luttinger-Sy模型。我们证明了理想玻色子气体在奇异点杂质泊松随机势中的一维模型中存在缩聚现象。为了处理非对角线长程阶，我们显式地计算了相应的空间平均单体约简密度矩阵。我们证明了该随机模型中玻色-爱因斯坦凝聚的数学机制类似于一维非随机比例间隔分层模型中的凝聚。对于Luttinger-Sy模型，我们证明了Kac-Luttinger猜想，即该模型在对数大小的单个“最大”区间内表现出I型BEC。
We present a rigorous study of the Bose-Einstein condensation in the Luttinger-Sy model. We prove the existence of the condensation in this one-dimensional model of the perfect boson gas placed in the Poisson random potential of singular point impurities. To tackle the off-diagonal long-range order we calculate explicitly the corresponding space-averaged one-body reduced density matrix. We show that mathematical mechanism of the Bose-Einstein condensation in this random model is similar to condensation in a one-dimensional nonrandom hierarchical model of scaled intervals. For the Luttinger-Sy model we prove the Kac-Luttinger conjecture, i.e., that this model manifests a type I BEC localized in a single "largest" interval of logarithmic size.