Superfluid-insulator transition in disordered boson systems

We review the localization problem in two dimensions for interacting bosons in a random potential. This problem is intimately related to the study of ⁴ He adsorbed in porous media, Josephson junction arrays, disordered superconducting films and vortex glasses. Using path integral Monte Carlo techniques, we find a superfluid, a localized or Bose glass insulator with gapless excitations, and (at commensurate densities) a Mott insulator with a finite gap to excitations.