It is found that a neutral particle acquires a nontrivial quantum phas
e independent of the paticlevelocity in crossed electric and magnetic
fields. It is proved that the phase is independent of the particle tra
jectory shape if the fields are homogeneous along a certain direction.
The phase induced by the crossed fields is shown to be responsible fo
r dissipation-free flows in superfluid systems, which are similar to t
he Meissner currents in superconductors.