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

TL;DR

This paper explores how the curvature of the single particle spectrum influences correlation functions in one-dimensional systems, revealing oscillatory Green's functions and partial support of polarization operators through quantum hydrodynamics and WKB methods.

Contribution

It introduces a novel analysis of the effects of spectrum curvature on correlation functions in one-dimensional quantum systems using hydrodynamic and WKB approaches.

Findings

Green's function exhibits oscillations due to spectrum curvature

Polarization operator has finite support in frequency-momentum space

Correlation functions are affected by periodic density waves

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.