The superfluid-Bose glass transition in a 1-D weakly interacting Bose gas

We study the one-dimensional Bose gas in spatially correlated disorder at T=0, using an extended density-phase Bogoliubov method. The decay of the one-body density matrix is analyzed and particular attention is paid to the behavior of the low-energy Bogoliubov excitations across the phase boundary. We have observed that the transition to the Bose glass phase is marked by a divergence in the density of states together with a 1/E behaviour of the localization length of the Bogoliubov modes. Finally we draw the phase diagram of the superfluid-insulator transition in the limit of small interaction strength.