Simulation of Lindblad equations for quarkonium in the quark-gluon plasma

TL;DR

This paper investigates the Lindblad equation's application to simulate quarkonium behavior in quark-gluon plasma, confirming thermalization and proposing an efficient computational method for large-scale heavy-ion collision simulations.

Contribution

It demonstrates the validity of Lindblad dynamics for quarkonium thermalization and introduces a dipole limit approach for computational efficiency.

Findings

Heavy quark recoils correctly thermalize quarkonium states.

The dipole limit Lindblad equation reduces numerical costs.

Simulation results match statistical expectations.

Abstract

We study the properties of the Lindbladian quantum mechanical evolution of quarkonia with non-Abelian charges (color-singlet and octet) in the quark-gluon plasma. We confirm that heavy quark recoils in the Lindblad equation correctly thermalize quarkonium colorful states within statistical errors from the simulation method. We also demonstrate that the Lindblad equation in the dipole limit can provide an efficient alternative method, which is applicable to a finite time evolution before thermalization and dramatically reduces the numerical cost. Our findings will serve as a foundation for large-scale simulation of quarkonium dynamics in the relativistic heavy-ion collisions.