Condensed Matter Theory

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.

Abstract:

Recent schemes for probing non-Abelian statistics in the quantum Hall effect are based on geometries where current-carrying quasiparticles flow along edges that encircle bulk quasiparticles, which are localized. Here we consider one such scheme, the Fabry-Perot interferometer, and analyze how its interference patterns are affected by a coupling that allows tunneling of neutral Majorana fermions between the bulk and edge. While at weak coupling this tunneling degrades the interference signal, we find that at strong coupling, the bulk quasiparticle becomes essentially absorbed by the edge and the intereference signal is fully restored. Furthermore, we find that the strength of the coupling can be tuned by the source-drain voltage. © 2008 The American Physical Society.

Abstract:

We show how the capillary filling of microchannels is affected by posts or ridges on the sides of the channels. Ridges perpendicular to the flow direction introduce contact line pinning, which slows, or sometimes prevents, filling, whereas ridges parallel to the flow provide extra surface that may enhance filling. Patterning the microchannel surface with square posts has little effect on the ability of a channel to fill for equilibrium contact angle theta_{e} less than approximately 30 degrees . For theta_{e} greater than approximately 60 degrees , however, even a small number of posts can pin the advancing liquid front.