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

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.

v1: 6 pages, 4 figures. v2: 11 pages, 8 figures, substantially updated from v1

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• Chromoelectric field correlator for quarkonium transport in the strongly coupled $\mathcal{N}=4$ Yang-Mills plasma from AdS/CFT
• Bottom energy loss and non-prompt $J/\psi$ production in relativistic heavy ion collisions
• Quarkonium dynamics in the quantum Brownian regime with non-abelian quantum master equations
• Generalized Gluon Distribution for Quarkonium Dynamics in Strongly Coupled $\mathcal{N}=4$ Yang-Mills Theory