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arXiv · 0806.2322

Excitations of the One Dimensional Bose-Einstein Condensates in a Random Potential

V. Gurarie·G. Refael·J. T. Chalker
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Abstract

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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V. Gurarie, G. Refael, J. T. Chalker. 2008-06-13. Excitations of the One Dimensional Bose-Einstein Condensates in a Random Potential. https://doi.org/10.1103/physrevlett.101.170407

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