  We find that correlation functions at one dimension are crucially affected by
the curvature of the bare single particle spectrum. Parabolic curvature leads
to two closely related phenomena: the Green's function exhibits oscillation (as
a function of the coordinate), while the polarization operator acquires support
in part of the frequency-momentum plane. We calculated the Green's function
using the WKB approximation for collective variables theory
\cite{JevickiSakita}. Within this approach, the single particle Green's
function is related to a quantum soliton \cite{Polychronakos}. The finite
support of the polarization operator is due to periodic density waves.
