The anomalous tunneling of Bose-condensate excitations
  We discuss the tunneling of phonon excitations across a potential barrier separating two condensate bulks. It is shown that the strong barrier proves to be transparent for the excitations at low energy $\epsilon$. Moreover, the transmission is reduced with increasing $\epsilon$ in contrast to the standard dependence. This anomalous behavior is due to an existence of the quasiresonance interaction. The origin of this interaction is a result of the formation of the special well determined by the density distribution of condensate in the vicinity of a high barrier. 
Yu.Kagan, D.L.Kovrizhin, and L.A.Maksimov