Dynamic structure factor of Calogero-Sutherland fluids

TL;DR

This paper analyzes the dynamic structure factor of Calogero-Sutherland fluids using an extended conformal field theory, revealing a sharp resonant response and confirming the equivalence of first and second quantized formulations.

Contribution

It provides a detailed comparison of the dynamic structure factor in different formulations, demonstrating their agreement and highlighting the role of algebraic structures in integrability.

Findings

Sharp response function peaked at one resonant frequency

Complete agreement between first and second quantized results

Supports the equivalence of different quantized treatments of the model

Abstract

The effective extended conformal field theory with symmetry W_infinity*{bar W_infinity} that describes the thermodynamic limit of the Calogero-Sutherland model is considered. The dynamic structure factor of the chiral component in the repulsive regime is determined and compared with the corresponding one of the free bosonic theory, given that both share isomorphic Hilbert spaces but differ in the time evolution of quantum states. In either case, a sharp response function peaked at only one resonant frequency is found, and the physical implications of this outcome are addressed. Furthermore, a detailed comparison between this result and the corresponding one obtained in the first quantized formulation of the Calogero-Sutherland model is provided. Complete agreement in the parameter region in which both results overlap is found. This outcome provides further support to the equivalence between the first and second quantized treatments of the Calogero-Sutherland model, in which the computational advantages from integrability in the first formulation are paralleled by those from the algebraic structure of the second.