Green's Function of Anyons in Calogero Model and Quantum Hydrodynamics

Abstract

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.