Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2008-06-13
Phys. Rev. Lett. 101, 170407 (2008)
Physics
Condensed Matter
Disordered Systems and Neural Networks
Scientific paper
10.1103/PhysRevLett.101.170407
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 $\ell(\omega)\sim 1/\omega^\alpha$. We show that the well known result $\alpha=2$ applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, $\alpha$ starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, $\alpha=1$. 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.
Chalker John T.
Gurarie Victor
Refael Gil
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