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

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.

5 pages, 1 figure

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• Collective fields, Calogero-Sutherland model and generalized matrix models
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• Waves and Solitons in the Continuum Limit of the Calogero-Sutherland Model
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