Initial distributions for local-equilibrium states

Determine the exact initial rapidity distribution \(\rho(x,0,\lambda)\) corresponding to local-equilibrium initial density matrices of the quantum and classical rational Calogero models, extending the specification beyond free-fermion limits.

Background

The transport equation derived in the paper requires an initial local density of states ρ(x,0,λ)\rho(x,0,\lambda). Although the microscopic Wigner-operator construction defines this distribution for any initial density matrix, the paper notes that an explicit characterization for local-equilibrium density matrices is not presently available beyond free-fermion cases.

Such a characterization would establish how generalized Gibbs-type initial states map to rapidity distributions, including the local-density approximation and its possible derivative corrections.

References

This requires converting an initial density matrix \hat{\rho} into its corresponding distribution function \rho(x,0,\lambda), a problem whose solution remains largely open beyond free-fermion limits.

— Microscopically exact transport equation for the quantum Calogero model  (2609.03018 - Bulchandani et al., 2 Sep 2026) in Section “Initial conditions and a consistency check”