From the universal Lindblad equation to Boltzmann equations: in-QGP quarkonium dynamics

How can the microscopic quantum dynamics of heavy quarkonium in the quark-gluon plasma (QGP), described by universal Lindblad equations, be systematically connected to semiclassical transport theory?

The researchers build upon recently derived coupled singlet-octet universal Lindblad equations (ULEs), which provide a unified quantum description of in-medium quarkonium independent of the traditional quantum Brownian and quantum optical regimes. They formulate these ULEs within the potential non-relativistic QCD (pNRQCD) effective field theory and take their semiclassical limit to obtain coupled singlet-octet Boltzmann equations. This approach avoids the rotating-wave approximation (RWA) and extends beyond the small-dipole limit, permitting the tracking of heavy-quark pairs from compact bound states to widely separated configurations.

The work delivers the first direct derivation of Boltzmann transport equations from the universal Lindblad framework. When taking the small-dipole limit, the resulting singlet Boltzmann equation nearly perfectly matches previous derivations based on the Davies secular equation and the rotating-wave approximation. However, the octet Boltzmann equation features an additional collision term—representing transitions within the continuum of octet scattering states—that is missing in RWA-based formulations. Additionally, the authors compute the leading-order quantum correction to the singlet Boltzmann equation, providing a more rigorous foundation for phenomenological QGP studies.

Quarkonia serve as crucial probes of the QGP produced in heavy-ion collisions. By establishing a bridge between open quantum systems and semiclassical transport without relying on restrictive approximations like the RWA or small-dipole limits, this work places the phenomenological description of quarkonium dissociation, regeneration, and diffusion on a much firmer and more general theoretical footing.