Effect of quasiparticle renormalization on the localization of the excitations of a one-dimensional Bose-Einstein condensate in a random potential

We investigate the effects of renormalization on the localization of the quasiparticle excitations of one-dimensional Bose-Einstein condensate in a random potential. Starting with a set of linearized equations of motion for the phases of superfluid grains coupled by Josephson interactions, we use mode-counting techniques to calculate the inverse localization length for large (10⁸) arrays. Employing distributions for the interaction parameters that are the same as the initial (pre-renormalization) distributions used by Gurarie et al. (Phys. Rev. Lett. 101 (2008) 170407), we compare the initial-interaction results for the localization length with those obtained using renormalization group techniques.