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

Collective field theory for the 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—the quantum integrable Benjamin-Ono equation. It renders tools of integrable systems to studies of nonlinear dynamics of 1D quantum liquids.