  It has been well known that quantum fluctuations induce a macroscopic phase
transition from a superfluid to a Mott insulator phase driven by the repulsive
potential energy in the ground state of dense bosonic systems on a lattice. We
find a quantum phase transition from the homogeneous to an inhomogeneous
Bose-condensate strongly affected or sometimes driven by the kinetic energy
dispersion in dilute bosonic superfluids, which provides a clear identification
of the superfluid state.
