Quasiparticle kinetic theory for Calogero models

We show that the quasiparticle kinetic theory for quantum and classical Calogero models reduces to free-streaming Boltzmann equation. reconcile this simple emergent behaviour with strongly interacting character of model by developing a Bethe-Lax correspondence in case. This demonstrates explicitly freely propagating degrees freedom are not bare particles, but rather quasiparticles corresponding eigenvectors Lax matrix. apply resulting particles external trapping potentials find excellent agreement numerical simulations all cases, both harmonic traps preserve integrability exhibit perfect revivals, anharmonic break microscopic integrability. Our framework also yields description multi-soliton solutions trap, solitons sharp peaks density. Extensions systems discussed.