Extension to integrable systems with velocity dressing

Extend the microscopic Wigner-operator methods developed for the rational Calogero model to integrable settings with velocity dressing, in particular the hyperbolic Calogero model.

Background

The rational Calogero model has no velocity dressing, which makes its exact transport equation free-streaming in rapidity. The paper identifies extension to systems with velocity dressing as a central unresolved direction because the conserved-charge Lax matrix and the rapidity-generating Lax matrix need not coincide.

The hyperbolic Calogero model is proposed as a particularly suitable test case because it is a continuum integrable system with a Lax pair but does exhibit velocity dressing.