Quantum Phase Transition from Superfluid to Localized Condensates of   Bose Fluid in a Confined Potential
  We develop a model of a strongly correlated Bose fluid model in a confined potential for the purpose of analyzing the localization of Bose-Einstein condensation and the disappearance of superfluidity. This work is motivated by the recent observation of a quantum phase transition in liquid $^4$He in porous glass at high pressures. By introducing a pressure-dependent localization length of the localized condensates, we could make a new analytical criterion for the localization of the condensate. Without introducing any free parameters, the resulting critical pressure of the transition from superfluid to localization is shown to be quantitatively consistent with observations. 
Michikazu Kobayashi and Makoto Tsubota