Low Temperature Relaxation of the Phase in an Inhomogeneous Bose Gas
  An effective action is obtained of a Bose gas in the bulk separated into two regions by a strong external potential depending on the single coordinate. The main attention is focused on the relaxation of the difference between phases of the weakly coupling condensates of the different bulk domains separated from each other by the external potential. The cases of low and high temperatures are considered. 
V.S.Babichenko