随机势场中一维玻色-爱因斯坦凝聚体的激发
Excitations of the One Dimensional Bose-Einstein Condensates in a Random Potential
摘要：
我们研究玻色子跳跃的一维晶格中存在的随机势在零温度。在这种条件下形成的玻色-爱因斯坦凝聚体的Bogoliubov激发是局域化的，局域化长度在低频发散为$\ell(ω)\sim 1/ω^α$。我们证明了著名的结果$α=2$只适用于足够弱的随机势。当随机势增加到超过一定强度时，$α$开始减小。在临界势强度下，当玻色子系统处于从超流到绝缘体的过渡时，$α=1$。这一结果对于理解原子玻色-爱因斯坦凝聚体在无规势作用下的行为以及无序约瑟夫森结阵列的行为是有意义的。
英文摘要：
We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as $\ell(ω)\sim 1/ω^α$. We show that the well known result $α=2$ applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, $α$ starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, $α=1$. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays.
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