Condensed Matter Theory

Abstract:

We use two different sub-gridscale lattice Boltzmann methods to simulate the swimming motion of a model swimmer. We systematically characterise the discretisation errors associated with placing a continuous object on a grid, and place limits on how low the Reynolds number needs to be in order to reach the characteristic zero Reynolds number regime. (C) 2008 Elsevier B.V. All rights reserved.

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 $\ell(\omega)\sim 1/\omega^\alpha$. 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.