Quantum Hydrodynamics, Quantum Benjamin-Ono Equation, and Calogero Model

TL;DR

This paper demonstrates that the quantum hydrodynamics of the Calogero model can be formulated as the quantum Benjamin-Ono equation, linking integrable systems to the nonlinear dynamics of 1D quantum liquids.

Contribution

It introduces a novel formulation of the Calogero model's quantum hydrodynamics as a single integrable Benjamin-Ono equation, enabling new analytical approaches.

Findings

Quantum hydrodynamics expressed as Benjamin-Ono equation

Connection between Calogero model and integrable systems

Potential for new studies of 1D quantum liquids

Abstract

Collective field theory for Calogero model represents particles with fractional statistics in terms of hydrodynamic modes -- density and velocity fields. We show that the quantum hydrodynamics of this model can be written as a single evolution equation on a real holomorphic Bose field -- quantum integrable Benjamin-Ono equation. It renders tools of integrable systems to studies of nonlinear dynamics of 1D quantum liquids.