  We show that zero-energy flows appear in many particle systems as same as in
single particle cases in 2-dimensions. Vortex patterns constructed from the
zero-energy flows can be investigated in terms of the eigenstates in conjugate
spaces of Gel'fand triplets. Stable patterns are written by the superposition
of zero-energy eigenstates. On the other hand vortex creations and
annihilations are described by the insertions of unstable eigenstates with
complex-energy eigenvalues into the stable patterns. Some concrete examples are
presented in the 2-dimensional parabolic potential barrier case. %, i.e., $-m
\gamma^2 (x^2+y^2)/2$. We point out three interesting properties of the
zero-energy flows; (i) the absolute economy as for the energy consumption, (ii)
the infinite variety of the vortex patterns, and (iii) the absolute stability
of the vortex patterns .
